Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus Enhanced with Graphing Utilities
In Problems 1-4, find the following for each pair of points: (a) The distance between the points. (b) The midpoint of the line segment connecting the points. (c) The slope of the line containing the points. (d) Then interpret the slope found in part (c). ( 0,0 ) ; ( 4,2 )In Problems 1-4, find the following for each pair of points: (a) The distance between the points. (b) The midpoint of the line segment connecting the points. (c) The slope of the line containing the points. (d) Then interpret the slope found in part (c). ( 1,1 ) ; ( 2,3 )In Problems 1-4, find the following for each pair of points: (a) The distance between the points. (b) The midpoint of the line segment connecting the points. (c) The slope of the line containing the points. (d) Then interpret the slope found in part (c). ( 4,4 ) ; ( 4,8 )In Problems 1-4, find the following for each pair of points: (a) The distance between the points. (b) The midpoint of the line segment connecting the points. (c) The slope of the line containing the points. (d) Then interpret the slope found in part (c). ( 2,1 ) ; ( 3,1 )List the intercepts of the following graph.6. Graph y= x 2 +15 using a graphing utility. Create a table of values to determine a good initial viewing window. Use a graphing utility to approximate the intercepts.In Problems 7-9, determine the intercepts and graph each equation by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. 2x3y=6In Problems 7-9, determine the intercepts and graph each equation by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. y= x 2 9In Problems 7-9, determine the intercepts and graph each equation by plotting points. Verify your results using a graphing utility. Label the intercepts on the graph. x 2 +2y=16In Problems 10-14, test each equation for symmetry with respect to the xaxis , the yaxis , and the origin. 2x=3 y 2In Problems 10-14, test each equation for symmetry with respect to the xaxis , the yaxis , and the origin. x 2 +4 y 2 =16In Problems 10-14, test each equation for symmetry with respect to the xaxis , the yaxis , and the origin. y= x 4 3 x 2 4In Problems 10-14, test each equation for symmetry with respect to the xaxis , the yaxis , and the origin. y= x 3 xIn Problems 10-14, test each equation for symmetry with respect to the xaxis , the yaxis , and the origin. x 2 +x+ y 2 +2y=0Sketch a graph of y= x 3 .In Problems 16 anti 17, use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between 10 and 10. x 3 5x+3=0In Problems 16 anti 17, use a graphing utility to approximate the solutions of each equation rounded to two decimal places. All solutions lie between 10 and 10. x 4 3=2x+1In Problems 18-25, find an equation of the line having the given characteristics. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Graph the line. Slope=2 ; containing the point ( 3,1 )In Problems 18-25, find an equation of the line having the given characteristics. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Graph the line. Slope=0 ; containing the point (5,4)In Problems 18-25, find an equation of the line having the given characteristics. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you prefer. Graph the line. Slope undefined; containing the point (3,4)x-intercept=2 ; containing the point ( 4,5 )y-intercept=2 ; containing the point ( 5,3 )Containing the points ( 3,4 ) and ( 2,1 )Parallel to the line 2x3y=4 ; containing the point ( 5,3 )Perpendicular to the line 3xy=4 ; containing the point ( 2,4 )26RE27RE28RE29RE30RE31REShow that the points A=( 2,0 ) , B=( 4,4 ) , and C=( 8,5 ) are the vertices of a right triangle in two ways: (a) By using the converse of the Pythagorean Theorem (b) By using the slopes of the lines joining the vertices31. Show that the points A=( 2,5 ) , B=( 6,1 ) , and C=( 8,1 ) lie on a straight line by using slopes.34RE35RE34. Find two numbers y such that the distance from ( 3,2 ) to ( 5,y ) is 10.35. Graph the line with slope 2 3 containing the point ( 1,2 ) .Make up four problems that you might be asked to do given the two points ( 3,4 ) and ( 6,1 ) . Each problem should involve a different concept. Be sure that your directions are clearly stated.37. Describe each of the following graphs in the xy -plane. Give justification. (a) x=0 (b) y=0 (c) x+y=0 (d) xy=0 (e) x 2 + y 2 =01CT2CT3CT4CT5CT6CT7CT8CT9CT10CT11CT12CT13CT1. On a real number line the origin is assigned the number _____ .2. If 3 and 5 are the coordinates of two points on the real number line, the distance between these points is _____ .3. If 3 and 4 are the legs of a right triangle, the hypotenuse is _____ .4. Use the converse of the Pythagorean Theorem to show that a triangle whose sides are of lengths 11, 60 and 61 is a right triangle.5. The area of a triangle whose base is b and whose altitude is h is A= _____ .6. True or False Two triangles are congruent if two angles and the included side of one equals two angles and the included side of the other.7. If ( x,y ) are the coordinates of a point P in the xy-plane , then x is called the _____ of P and y is the _____ of P .8. The coordinate axes divide the xy-plane into four sections called _____ .9. If three distinct points P , Q and R all lie on a line and if d( P,Q )=d(Q,R) , then Q is called the _____ of the line segment from P to R .10. True or False The distance between two points is sometimes a negative number.11. True or False The point (1,4) lies in quadrant IV of the Cartesian plane.12. True or False The midpoint of a line segment is found by averaging the x-coordinates and averaging the y-coordinates of the endpoints.In Problems 15 and 16, plot each point in the xy-plane . Tell in which quadrant or on what coordinate axis each point lies. 15. (a) A=( 3,2 ) (b) B=( 6,0 ) (c) C=( 2,2 ) (d) D=( 6,5 ) (e) E=( 0,3 ) (f) F=( 6,3 )In Problems 15 and 16, plot each point in the xy-plane . Tell in which quadrant or on what coordinate axis each point lies. 16. (a) A=( 1,4 ) (b) B=( 3,4 ) (c) C=( 3,4 ) (d) D=( 4,1 ) (e) E=( 0,1 ) (f) F=( 3,0 )17. Plot the points ( 2,0 ),( 2,3 ),( 2,4 ),(2,1) and ( 2,1 ) . Describe the set of all points of the form ( 2,y ) , where y is a real number.18. Plot the points ( 0,3 ),( 1,3 ),( 2,3 ),(5,3) and ( 4,3 ) . Describe the set of all points of the form ( x,3 ) , where x is a real number.In Problems 19-22, determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers. 19.In Problems 19-22, determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers. 20.In Problems 19-22, determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers. 21.In Problems 19-22, determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers. 22.In Problems 23-28, select a setting so that each given point will lie within the viewing window. 23. ( 10,5 ),( 3,2 ),( 4,1 )In Problems 23-28, select a setting so that each given point will lie within the viewing window. 24. ( 5,0 ),( 6,8 ),( 2,3 )In Problems 23-28, select a setting so that each given point will lie within the viewing window. 25. ( 40,20 ),( 20,80 ),( 10,40 )In Problems 23-28, select a setting so that each given point will lie within the viewing window. 26. ( 80,60 ),( 20,30 ),( 20,40 )In Problems 23-28, select a setting so that each given point will lie within the viewing window. 27. ( 0,0 ),( 100,5 ),( 5,150 )In Problems 23-28, select a setting so that each given point will lie within the viewing window. 28. ( 0,1 ),( 100,50 ),( 10,30 )In Problems 29-34, determine the viewing window used. 29.In Problems 29-34, determine the viewing window used. 30.In Problems 29-34, determine the viewing window used. 31.In Problems 29-34, determine the viewing window used. 32.In Problems 29-34, determine the viewing window used. 33.In Problems 29-34, determine the viewing window used. 34.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 35.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 36.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 37.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 38.In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 39. P 1 =( 3,4 ); P 2 =( 5,4 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 40. P 1 =( 1,0 ); P 2 =( 2,4 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 41. P 1 =( 5,3 ); P 2 =( 11,9 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 42. P 1 =( 2,3 ); P 2 =( 10,3 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 43. P 1 =( 4,3 ); P 2 =( 6,4 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 44. P 1 =( 4,3 ); P 2 =( 6,2 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 45. P 1 =( a,b ); P 2 =( 0,0 )In Problems 35-46, find the distance d( P 1 , P 2 ) between the points P 1 and P 2 . 46. P 1 =( a,a ); P 2 =( 0,0 )In Problems 47-50, find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates. 47.In Problems 47-50, find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates. 48.In Problems 47-50, find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates. 49.In Problems 47-50, find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates. 50.In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 51. A=( 2,5 );B=( 1,3 );C=( 1,0 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 52. A=( 2,5 );B=( 12,3 );C=( 10,11 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 53. A=( 5,3 );B=( 6,0 );C=( 5,5 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 54. A=( 6,3 );B=( 3,5 );C=( 1,5 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 55. A=( 4,3 );B=( 0,3 );C=( 4,2 )In Problems 51-56, plot each point and form the triangle ABC . Verify that the triangle is a right triangle. Find its area. 56. A=( 4,3 );B=( 4,1 );C=( 2,1 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 57. P 1 =( 3,4 ); P 2 =( 5,4 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 58. P 1 =( 2,0 ); P 2 =( 2,4 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 59. P 1 =( 5,3 ); P 2 =( 11,9 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 60. P 1 =( 2,3 ); P 2 =( 10,3 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . 61. P 1 =( 4,3 ); P 2 =( 6,1 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( 4,3 ); P 2 =( 2,2 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( a,b ); P 2 =( 0,0 )In Problems 57-64, find the midpoint of the line segment joining the points P 1 and P 2 . P 1 =( a,a ); P 2 =(0,0)In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: y= x 4 x Points: ( 0,0 );( 1,1 );( 1,0 )In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: y= x 3 2x Points: ( 0,0 );( 1,1 );( 1,1 )In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: y 2 = x 2 +9 Points: ( 0,3 );( 3,0 );( 3,0 )In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: y 3 =x+1 Points: ( 1,2 );( 0,1 );( 1,0 )In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: x 2 + y 2 =4 Points: ( 0,2 );( 2,2 );( 2,2 )In Problems 65-70, tell whether the given points are on the graph of the equation. Equation: x 2 +4 y 2 =4 Points: ( 0,1 );( 2,0 );( 2, 1 2 )In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 71-78, the graph of an equation is given. List the intercepts of the graph.In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y=x+2In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y=x6In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y=2x+8In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y=3x9In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y= x 2 1In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y= x 2 9In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y= x 2 +4In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y= x 2 +1In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. 2x+3y=6In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. 5x+2y=10In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. 9 x 2 +4y=36In Problems 79-90, graph each equation by plotting points. Verify your results using a graphing utility. y=2x13In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. y=2x13In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. y=3x+14In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. y=2 x 2 15In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. y=3 x 2 +19In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. 3x2y=43In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. 4x+5y=82In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. 5 x 2 +3y=37In Problems 91-98, graph each equation using a graphing utility. Use a graphing utility to approximate the intercepts rounded to two decimal places. Use the TABLE feature to help to establish the viewing window. 2 x 2 3y=35If the point ( 2,5 ) is shifted 3 units right and 2 units down, what are its new coordinates?fIf the point ( 1,6 ) is shifted 2 units left and 4 units up, what are its new coordinates?The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side (see the figure). Find the lengths of the medians of the triangle with vertices at A=( 0,0 ),B=( 6,0 ),andC=( 4,4 ) .An equilateral triangle is one in which all three sides are of equal length. If two vertices of an equilateral triangle are ( 0,4 )and( 0,0 ) , find the third vertex. How many of these triangles are possible?In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 2,1 ); P 2 =( 4,1 ); P 3 =( 4,3 )In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =(1,4); P 2 =(6,2); P 3 =(4,5)In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 2,1 ); P 2 =( 0,7 ); P 3 =( 3,2 )In Problems 103-106, find the length of each side of the triangle determined by the three points P 1 , P 2 ,and P 3 . State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P 1 =( 7,2 ); P 2 =( 4,0 ); P 3 =( 4,6 )Baseball A major league baseball “diamond� is actually a square, 90 feet on a side (see the figure). What is the distance directly from home plate to second base (the diagonal of the square)?Little league Baseball The layout of a Little League playing field is a square, 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)? Source: Little League Baseball, Official Regulations and Playing Rules, 2014.Baseball Refer to Problem 109. Overlay a rectangular coordinate system on a major league baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. (a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. (b) If the right fielder is located at ( 310,15 ) , how far is it from there to second base? (c) If the center fielder is located at ( 300,300 ) , how far is it from there to third base?Little League Baseball Refer to Problem 110. Overlay a rectangular coordinate system on a Little League baseball diamond so that the origin is at home plate, the positive x-axis lies in the direction from home plate to first base, and the positive y-axis lies in the direction from home plate to third base. (a) What are the coordinates of first base, second base, and third base? Use feet as the unit of measurement. (b) If the right fielder is located at ( 180,20 ) , how far is it from there to second base? (c) If the center fielder is located at ( 220,220 ) , how far is it from there to third base?Distance between Moving Objects A Ford Focus and a Freightliner truck leave an intersection at the same time. The Focus heads east at an average speed of 30 miles per hour, while the truck heads south at an average speed of 40 miles per hour. Find an expression for their distance apart d (in miles) at the end of t hours.Distance of a Moving Object from a Fixed Point A hot-air balloon, headed due east at an average speed of 15 miles per hour at a constant altitude of 100 feet, passes over an intersection (see the figure). Find an expression for its distance d (measured in feet) from the intersection t seconds later.Drafting Error When a draftsman draws three lines that are to intersect at one point, the lines may not intersect as intended and subsequently will form an error triangle. If this error triangle is long and thin, one estimate for the location of the desired point is the midpoint of the shortest side. The figure shows one such error triangle. Find an estimate for the desired intersection point. Find the length of the median for the midpoint found in part (a). See Problem 101.Net Sales The figure illustrates how net sales of Wal-Mart Stores, Inc., have grown from 2011 through 2015. Use the midpoint formula to estimate the net sales of Wal-Mart Stores, Inc., in 2013. How does your result compare to the reported value of 469 billion? Source: Wal-Mart Stores, Inc., 2015 Annual ReportPoverty Threshold Poverty thresholds arc determined by the U.S. Census Bureau. A poverty threshold represents the minimum annual household income for a family not to be considered poor. In 2005, the poverty threshold for a family of four with two children under the age of 18 years was 19,350 . In 2015, the poverty threshold for a family of four with two children under the age of 18 years was 24,250 . Assuming poverty thresholds increase in a straight-line fashion, use the midpoint formula to estimate the poverty threshold of a family of four with two children under the age of 18 in 2010. How does your result compare to the actual poverty threshold in 2010 of 22,050 ? Source: U.S Census BureauIn Problem 118, you may use a graphing utility, but it is not required. (a) Graph y= x 2 ,y=x,y=| x |andy= ( x ) 2 , noting which graphs are the same. (b) Explain why the graphs of y= x 2 andy=| x | are the same. (c) Explain why the graphs of y=xandy= ( x ) 2 are not the same. (d) Explain why the graphs of y= x 2 andy=x are not the same.115AYUMake up an equation satisfied by the ordered pairs ( 2,0 ),( 4,0 ),and( 0,1 ) . Compare your equation with a friend’s equation. Comment on any similarities.Draw a graph that contains the points ( 2,1 ),( 0,1 ),( 1,3 )and( 3,5 ) . Compare your graph with those of other students. Are most of the graphs almost straight lines? How many are “curved�? Discuss the various ways that these points might be connected.Explain what is meant by a complete graph.Write a paragraph that describes a Cartesian plane. Then write a second paragraph that describes how to plot points in the Cartesian plane. Your paragraphs should include the terms “coordinate axes,� “ordered pair,� “coordinates,� “plot,� “ x-coordinate ,� and “ y-coordinate .�Solve: 2( x+3 )1=7 (pp. A44-A46)Solve: x 2 4x12=0 (pp. A46-A52)The points, if any, at which a graph crosses or touches the coordinate axes are called _______.4AYU5AYU6AYUTrue or False To find the y-intercepts of the graph of an equation, let x=0 and solve for y .True or False If a graph is symmetric with respect to the x-axis , then it cannot be symmetric with respect to the y-axis .To find the x-intercept( s ) , if any, of the graph of an equation, let _______ in the equation and solve for x . (a) y=0 (b) x=0 (c) y=x (d) x=yTo test whether the graph of an equation is symmetric with respect to the origin, replace ______ in the equation and simplify. If an equivalent equation results, then the graph is symmetric with respect to the origin. (a) xbyx (b) ybyy (c) xbyxandybyy (d) xbyyandybyxIn Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=x+2In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=x6In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=2x+8In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y=3x9In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 1In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 9In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 +4In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. y= x 2 +1In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 2x+3y=6In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 5x+2y=10In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 9 x 2 +4y=36In Problems 11-22, find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. 4 x 2 +y=4In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,4)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (5,3)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (2,1)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (4,2)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (5,2)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (1,1)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,4)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (4,0)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (0,3)In Problems 23-32, plot each point. Then plot the point that is symmetric to it with respect to (a) the x-axis ; (b) the y-axis ; (c) the origin. (3,0)In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.In Problems 33-44, the graph of an equation is given. (a) Find the intercepts. (b) Indicate whether the graph is symmetric with respect to the x-axis , the y-axis , or the origin.45AYU46AYU47AYU48AYUIn Problems 49-64, list the intercepts and test for symmetry. y 2 =x+4In Problems 49-64, list the intercepts and test for symmetry. y 2 =x+9In Problems 49-64, list the intercepts and test for symmetry. y= x 3In Problems 49-64, list the intercepts and test for symmetry. y= x 5In Problems 49-64, list the intercepts and test for symmetry. y= x 4 8 x 2 9In Problems 49-64, list the intercepts and test for symmetry. y= x 4 2 x 2 8In Problems 49-64, list the intercepts and test for symmetry. 9 x 2 +4 y 2 =36In Problems 49-64, list the intercepts and test for symmetry. 4 x 2 + y 2 =4In Problems 49-64, list the intercepts and test for symmetry. y= x 3 27In Problems 49-64, list the intercepts and test for symmetry. y= x 4 1In Problems 49-64, list the intercepts and test for symmetry. y= x 2 3x4In Problems 49-64, list the intercepts and test for symmetry. y= x 2 +4In Problems 49-64, list the intercepts and test for symmetry. y= 3x x 2 +9In Problems 49-64, list the intercepts and test for symmetry. y= x 2 4 2xIn Problems 49-64, list the intercepts and test for symmetry. y= x 3 x 2 9In Problems 49-64, list the intercepts and test for symmetry. y= x 4 4 +1 2 x 5In Problems 65-68, draw a quick sketch of each equation. y= x 3In Problems 65-68, draw a quick sketch of each equation. x= y 2In Problems 65-68, draw a quick sketch of each equation. y= xIn Problems 65-68, draw a quick sketch of each equation. y= 1 xIf (3,b) is a point on the graph of y=4x+1 , what is b ?If (2,b) is a point on the graph of 2x+3y=2 , what is b ?If (a,4) is a point on the graph of y= x 2 +3x , what is a ?If (a,5) is a point on the graph of y= x 2 +6x , what is a ?In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. y= x 2 5In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. y= x 2 8In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. x y 2 =9In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. x+ y 2 =4In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. x 2 + y 2 =9In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. x 2 + y 2 =16In Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. y= x 3 4xIn Problems 73-80, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. y= x 3 x81AYUIf the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept .If the graph of an equation is symmetric with respect to the origin and 4 is an x-intercept of this graph, name another x-intercept .84AYU85AYU86AYUDraw a graph of an equation that contains two x-intercepts at one the graph crosses the x-axis , and at the other the graph touches the x-axis .88AYUDraw a graph that contains the points ( 2,1 ) , ( 0,1 ) , ( 1,3 ) , and ( 3,5 ) . Compare your graph with those of other students. Are most of the graphs almost straight lines? How many are “curved�? Discuss the various ways that these points might be connected.Draw a graph that contains the points ( 2,5 ) , ( 1,3 ) , and ( 0,2 ) that is symmetric with respect to the y-axis . Compare your graph with those of other students; comment on any similarities. Can a graph contain these points and be symmetric with respect to the x-axis ? the origin? Why or why not?Solve the equation 2 x 2 +5x+2=0 . (pp. A46-A52)Solve the equation 2x+3=4(x1)+1 . (pp. A44-A46)To solve an equation of the form { expressioninx }=0 using a graphing utility, we graph Y 1 ={ expressioninx } and use ______ to determine each x-intercept of the graph.True or False In using a graphing utility to solve an equation, exact solutions are always obtained.In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. x 3 4x+2=0In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. x 3 8x+1=0In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. 2 x 4 +5=3x2In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. x 4 +1=2 x 2 3In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. x 4 2 x 3 +3x1=0In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. 3 x 4 x 3 +4 x 2 5=011AYU12AYU13AYU14AYUIn Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. x 4 5 x 2 +2x+11=0In Problems 5-16, use a graphing utility to approximate the real solutions, if any, of each equation rounded to two decimal places. All solutions lie between -10 and 10. 3 x 4 +8 x 2 2x9=0In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 2(3+2x)=3(x4)In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 3(2x)=2x1In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 8x(2x+1)=3x13In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 5(2x1)=10xIn Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x+1 3 + x+2 7 =5In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 2x+1 3 +16=3xIn Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 5 y + 4 y =3In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 4 y 5= 18 2yIn Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. (x+7)(x1)= (x+l) 226AYUIn Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x 2 3x28=0In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x 2 7x18=0In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 3 x 2 =4x+430AYUIn Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x 3 + x 2 4x4=0In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x 3 +2 x 2 9x18=0In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x+1 =4In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. x2 =3In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 2 x+2 + 3 x1 = 8 5In Problems 17-36, solve each equation algebraically. Verify your solution using a graphing utility. 2 x+2 + 3 x1 = 8 5The slope of a vertical line is ______; the slope of a horizontal line is ______.For the line 2x+3y=6 , the x-intercept is ______ and the y-intercept is ______.3AYU