Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
76AYU77AYU78AYU79AYU80AYU81AYU82AYU83AYU84AYU85AYU86AYU87AYU88AYU89AYU90AYU91AYU92AYU93AYU94AYU95AYU96AYU97AYU98AYU99AYU100AYU101AYU102AYU103AYU104AYU105AYU106AYU107AYU108AYU109AYU110AYU111AYU112AYU113AYU114AYU115AYU116AYU117AYU118AYU119AYU120AYU121AYUTrue or False The quotient of two polynomial expressions is a rational expression, (p. A35)What are the quotient and remainder when 3 x 4 x 2 is divided by x 3 x 2 +1 . (pp. A25- A27)Graph y= 1 x .(pp.22-23)Graph y=2 ( x+1 ) 2 3 using transformations.(pp.106-114)True or False The domain of every rational function is the set of all real numbers.If, as x or as x , the values of R( x ) approach some fixed number L , then the line y=L is a _____ of the graph of R .If, as x approaches some number c , the values of | R( x ) | , then the line x=c is a ______ of the graph of R .For a rational function R , if the degree of the numerator is less than the degree of the denominator, then R is _____.9AYUTrue or False The graph of a rational function may intersect a horizontal asymptote.True or False If the degree of the numerator of a rational function equals the degree of the denominator, then the ratio of the leading coefficients gives rise to the horizontal asymptote.If a rational function is proper, then _____ is a horizontal asymptote.In Problems 15-26, find the domain of each rational function R( x )= 4x x3In Problems 15-26, find the domain of each rational function R( x )= 5 x 2 3+xIn Problems 15-26, find the domain of each rational function G( x )= 6 ( x+3 )( 4x )In Problems 15-26, find the domain of each rational function H( x )= 4 x 2 ( x2 )( x+4 )In Problems 15-26, find the domain of each rational function Q( x )= x(1x) 3 x 2 +5x2In Problems 15-26, find the domain of each rational function F( x )= 3x(x1) 2 x 2 5x3In Problems 15-26, find the domain of each rational function R( x )= x x 4 1In Problems 15-26, find the domain of each rational function R( x )= x x 3 8In Problems 15-26, find the domain of each rational function G( x )= x3 x 4 +1In Problems 15-26, find the domain of each rational function H( x )= 3 x 2 +x x 2 +4In Problems 15-26, find the domain of each rational function F( x )= 2( x 2 4 ) 3( x 2 +4x+4 )In Problems 15-26, find the domain of each rational function R( x )= 3( x 2 x6 ) 4( x 2 9 )In Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 27-32, use the graph shown to find a. The domain and range of each function b. The intercepts, if any c. Horizontal asymptotes, if any d. Vertical asymptotes, if any e. Oblique asymptotes, if anyIn Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. F( x )=2+ 1 xIn Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. Q( x )=3+ 1 x 2In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 3 xIn Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R(x)= 1 ( x1 ) 2In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. G( x )= 2 (x+2) 2In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. H( x )= 2 x+1In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 1 x1 +1In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= 1 x 2 +4x+4In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. F( x )=2 1 x+1In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. G( x )=1+ 2 (x3) 2In Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= x4 xIn Problems 33-44, (a) graph the rational function using transformations, (b) use the final graph to find the domain and range, and (c) use the final graph to list any vertical, horizontal, or oblique asymptotes. R( x )= x 2 4 x 2In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 3x+5 x-6In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 3x x+4In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. G( x )= x 3 +1 x 2 -5x-14In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. H( x )= x 3 -8 x 2 -5x+6In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. P( x )= 4 x 2 x 3 -1In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. T( x )= x 3 x 4 -1In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. Q( x )= 2 x 2 -5x-12 3 x 2 -11x-4In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. F( x )= x 2 +6x+5 2 x 2 +7x+5In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. R( x )= 8 x 2 +26x-7 4x-1In problems , (a) graph the rational function using transformation , (b) use the final graph to find the domain and range , and (c) use the final graph to list any vertical , horizontal, or
Oblique asymptotes.
In Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. G( x )= x 4 -1 x 2 -xIn Problems 45-56, find the vertical, horizontal, and oblique asymptotes, if any, of each rational function. F( x )= x 4 -16 x 2 -2x55AYU56AYU57AYU58AYU59AYU60AYU61AYU62AYU1AYU2AYU3AYU4AYU5AYU6AYUIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x+1 x( x+4 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x ( x1 )( x+2 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3x+3 2x+4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 2x+4 x1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3 x 2 4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 6 x 2 x6In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. P( x )= x 4 + x 2 +1 x 2 1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. Q( x )= x 4 1 x 2 4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 3 1 x 2 9In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x 3 +1 x 2 +2xIn Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 x 2 +x6In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x 2 4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x x 2 4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= 3x x 2 1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 3 ( x1 )( x 2 4 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 4 ( x+1 )( x 2 9 )In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 2 1 x 4 16In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. H( x )= x 2 +4 x 4 1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 3x4 x+2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 +3x+2 x1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x4In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 x12 x+5In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. F( x )= x 2 +x12 x+2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. G( x )= x 2 x12 x+1In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x ( x1 ) 2 ( x+3 ) 3In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= ( x1 )( x+2 )( x3 ) x ( x4 ) 2In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x12 x 2 x6In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +3x10 x 2 +8x+15In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 6 x 2 7x3 2 x 2 7x+6In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= 8 x 2 +26x+15 2 x 2 x15In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +5x+6 x+3In Problems 7-50, follow Steps 1 through 7 on page 234 to analyze the graph of each function. R( x )= x 2 +x30 x+639AYU40AYU41AYU42AYU43AYU44AYUIn Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)In Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)In Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)In Problems 51-54, find a rational function that might have the given graph. (More than one answer might be possible.)49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYUGraph each of the following functions: y= x 2 1 x1 y= x 3 1 x1 y= x 4 1 x1 y= x 5 1 x1 Is x=1 a vertical asymptote? Why not? What is happening for x=1 ? What do you conjecture about y= x n 1 x1 ,n1 an integer, for x=1 ?Graph each of the following functions: y= x 2 x1 y= x 4 x1 y= x 6 x1 y= x 8 x1 What similarities do you see? What differences?Create a rational function that has the following characteristics: crosses the x-axis at 3; touches the x-axis at 2 ; one vertical asymptote, x=1 ; and one horizontal asymptote, y=2 . Give your rational function to a fellow classmate and ask for a written critique of your rational function.Create a rational function that has the following characteristics: crosses the x-axis at 2; touches the x-axis at 1 ; one vertical asymptote at x=5 and another at x=6 ; and one horizontal asymptote, y=3 . Compare your function to a fellow classmate's. How do they differ? What are their similarities?Write a few paragraphs that provide a general strategy for graphing a rational function. Be sure to mention the following: proper, improper, intercepts, and asymptotes.Create a rational function with the following characteristics: three real zeros, one of multiplicity 2; y-intercept 1; vertical asymptotes, x=2andx=3 ; oblique asymptote, y=2x+1 . Is this rational function unique? Compare your function with those of other students. What will be the same as everyone else’s? Add some more characteristics, such as symmetry or naming the real zeros. How does this modify the rational function?Explain the circumstances under which the graph of a rational function will have a hole.Solve the inequality 34x5 . Graph the solution set. (pp. A79-A80)Solve the inequality x 2 5x24 . Graph the solution set. (pp. 170-172)3AYUTrue or False The graph of f( x )= x x3 is above the x-axis for x0 or x3 , so the solution set of the inequality x x3 0 is { x| x0orx3 } .In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 5-8, use the graph of the function f to solve the inequality. (a) f( x )0 (b) f( x )0In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= x 2 ( x3 ) .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=x ( x+2 ) 2 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= ( x+4 ) 2 ( 1x ) .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=( x1 ) ( x+3 ) 2 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )=2( x+2 ) ( x2 ) 3 .In Problems 9-14, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 81-86 of Section 4.1.] Solve f( x )0 , where f( x )= 1 2 ( x+4 ) ( x1 ) 3 .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= x+1 x( x+4 ) .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= x ( x1 )( x+2 ) .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= 3x+3 2x+4 .In Problems 15-18, solve the inequality by using the graph of the function. [Hint: The graphs were drawn in Problems 7-10 of Section 4.5.] Solve R( x )0 , where R( x )= 2x+4 x1 .19AYUIn Problems 19-48, solve each inequality algebraically. ( x-5 ) ( x+2 ) 2 0In Problems 19-48, solve each inequality algebraically. x 3 -4 x 2 0In Problems 19-48, solve each inequality algebraically. x 3 +8 x 2 0In Problems 19-48, solve each inequality algebraically. 2 x 3 -8 x 2In Problems 19-48, solve each inequality algebraically. 3 x 3 -15 x 2In problems 1954, solve each inequality algebraically. (x+2)(x4)(x6)0In Problems 19-48, solve each inequality algebraically. ( x-5 ) 2 ( x+2 )0In problems 1954, solve each inequality algebraically. x34x212x0In Problems 19-48, solve each inequality algebraically. x 3 +2 x 2 -3x0In Problems 19-48, solve each inequality algebraically. x 4 x 2In Problems 19-48, solve each inequality algebraically. x 4 9 x 2In Problems 19-48, solve each inequality algebraically. x 4 1In Problems 19-48, solve each inequality algebraically. x 3 133AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYU45AYU46AYU47AYU48AYU49AYU50AYU51AYU52AYU53AYU54AYU55AYU56AYU57AYU58AYU59AYU60AYUFor what positive numbers will the cube of a number exceed four times its square?For what positive numbers will the cube of a number be less than the number?What is the domain of the function f( x )= x 4 -16 ?What is the domain of the function f( x )= x 3 -3 x 2 ?What is the domain of the function f( x )= x-2 x+4 ?What is the domain of the function f( x )= x-1 x+4 ?67AYU68AYU69AYU70AYUAverage Cost Suppose that the daily cost C of manufacturing bicycles is given by C(x)=80x+5000 . Then the average daily cost C is given by C (x)= 80x+5000 x . How many bicycles must be produced each day for the average cost to be no more than 100 ?Average Cost See Problem 77. Suppose that the government imposes a 1000 -per-day tax on the bicycle manufacturer so that the daily cost C of manufacturing x bicycles is now given by C(x)=80x+6000 . Now the average daily cost C is given by C (x)= 80x+6000 x . How many bicycles must be produced each day for the average cost to be no more than 100 ?73AYU74AYU75AYU76AYU77AYU78AYU79AYU1. Find f( 1 ) if f( x )=2 x 2 x2. Factor the expression 6 x 2 +x-23. Find the quotient and remainder if 3 x 4 -5 x 3 +7x4 is divided by x3 . (pp. A25-A27 or A31-A34)4AYU5AYU6AYU7AYU8AYU9AYU10AYUIn Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 11. f( x )=4 x 3 -3 x 2 -8x+4 ; x-2In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 12. f( x )=-4 x 3 +5 x 2 +8 ; x+3In Problems , use the Remainder Theorem to find the remainder when
is divided by . Then use the Factor Theorem to determine whether is a factor of .
13.
In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 14. f( x )=4 x 4 -15 x 2 -4 ; x-2In Problems , use the Remainder Theorem to find the remainder when
is divided by . Then use the Factor Theorem to determine whether is a factor of .
15.
In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 16. f( x )=2 x 6 -18 x 4 + x 2 -9 ; x+3In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 17. f( x )=4 x 6 -64 x 4 + x 2 -15 ; x+4In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 18. f( x )= x 6 -16 x 4 + x 2 ; x+4In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 19. f( x )=2 x 4 - x 3 +2x-1 ; x- 1 2In Problems 11-20, use the Remainder Theorem to find the remainder when f( x ) is divided by x-c . Then use the Factor Theorem to determine whether x-c is a factor of f( x ) . 20. f( x )=3 x 4 + x 3 -3x+1 ; x+ 1 3In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 21. f( x )=-4 x 7 + x 3 - x 2 +2In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 22. f( x )=5 x 4 +2 x 2 -6x-5In Problems, determine the maximum number of real zeros that each polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros each polynomial function may have. Do not attempt to find the zeros.
23.
In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 24. f( x )=-3 x 5 +4 x 4 +2In Problems 2132, determine the maximum number of real zeros that each polynomial function may have. Then use Descartes' Rule of Signs to determine how many positive and how many negative real zeros each polynomial function may have. Do not attempt to find the zeros. f(x)=2x3+5x2x7In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 26. f( x )=- x 3 - x 2 +x+1In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 27. f( x )=- x 4 + x 2 -1In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 28. f( x )= x 4 +5 x 3 -2In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 29. f( x )= x 5 + x 4 + x 2 +x+1In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 30. f( x )= x 5 - x 4 + x 3 - x 2 +x-1In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 31. f( x )= x 6 -1In Problems 21-32, use Descartes' Rule of Signs to determine how many positive and how many negative zeros each polynomial function may have. Do not attempt to find the zeros. 32. f( x )= x 6 +1In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 33. f( x )=3 x 4 -3 x 3 + x 2 -x+1In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 34. f( x )= x 5 - x 4 +2 x 2 +3In Problems 3344, list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. f(x)=x52x2+8x5In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 36. f( x )=2 x 5 - x 4 - x 2 +1In Problems 3344, list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. f(x)=9x3x2+x+3In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 38. f( x )=6 x 4 - x 2 +2In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 39. f( x )=6 x 4 - x 2 +9In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 40. f( x )=-4 x 3 + x 2 +x+6In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 41. f( x )=2 x 5 - x 3 +2 x 2 +12In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 42. f( x )=3 x 5 - x 2 +2x+18In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 43. f( x )=6 x 4 +2 x 3 - x 2 +20In Problems 33-44, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros. 44. f( x )=-6 x 3 - x 2 +x+10In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 51. f( x )= x 3 +2 x 2 -5x-6In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 52. f( x )= x 3 +8 x 2 +11x-20In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x3x2+2x1In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x3+x2+2x+1In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=2x34x210x+20In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=3x3+6x215x30