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x+1 16. Sketch the graph of y showing clearly the intercepts and the behavior of the curve near X-1 its asymptotes.

x+1 16. Sketch the graph of y showing clearly the intercepts and the behavior of the curve near X-1 its asymptotes.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Answer Q16, 17

11. Sketch the curve given parametrically by the equation x = 1 + t, y = 1 – t. Plot on your sketch the point where the curve crosses the coordinates axis and the stationary point. Show that an equation of normal to curve at the point with .3 parameter is x – 2ty = 2t – 7t + 1. The normal to the curve at the point P where t = 1 cuts the | - curve again at point Q. determine the coordinates of Q. 3x-1 12. The function f is defined by f(x) X # 1 (x-1)2 ' a) Sketch the graph of f(x) showing clearly the coordinates of the turning point(s) and its behavior as it approaches its asymptotes. b) Show that the area of the finite région bounded by the curve and the lines x = 4 and y = 2 is =+ 21n. a+bx 13. The graph of has a turning point at p(2, -1). Find the values of a and b and hence, (x-1)(x-4)' sketch the curve y = f(x) showing clearly the turning points, asymptotes and intercept(s) with the axis. 14. Sketch the curve showing clearly the turning point(s) where the curve, meets the (x+1)(x-3) coordinates axis and the behavior of the curve near it asymptotes. 15. Sketch the graph of 2(x-1) showing clearly the point(s) where the curve meets the coordinates axis and the behavior of the curve near it asymptotes. X+1 16. Sketch the graph of y showing clearly the intercepts and the behavior of the curve near X-1 its asymptotes. 17. Sketch the curve of y x+2 %3D x ER, x + -1, showing clearly its intercepts with the coordinate axes x+1 and the behaviour of the curve as it approaches its asymptotes 2/3
Transcribed Image Text:11. Sketch the curve given parametrically by the equation x = 1 + t, y = 1 – t. Plot on your sketch the point where the curve crosses the coordinates axis and the stationary point. Show that an equation of normal to curve at the point with .3 parameter is x – 2ty = 2t – 7t + 1. The normal to the curve at the point P where t = 1 cuts the | - curve again at point Q. determine the coordinates of Q. 3x-1 12. The function f is defined by f(x) X # 1 (x-1)2 ' a) Sketch the graph of f(x) showing clearly the coordinates of the turning point(s) and its behavior as it approaches its asymptotes. b) Show that the area of the finite région bounded by the curve and the lines x = 4 and y = 2 is =+ 21n. a+bx 13. The graph of has a turning point at p(2, -1). Find the values of a and b and hence, (x-1)(x-4)' sketch the curve y = f(x) showing clearly the turning points, asymptotes and intercept(s) with the axis. 14. Sketch the curve showing clearly the turning point(s) where the curve, meets the (x+1)(x-3) coordinates axis and the behavior of the curve near it asymptotes. 15. Sketch the graph of 2(x-1) showing clearly the point(s) where the curve meets the coordinates axis and the behavior of the curve near it asymptotes. X+1 16. Sketch the graph of y showing clearly the intercepts and the behavior of the curve near X-1 its asymptotes. 17. Sketch the curve of y x+2 %3D x ER, x + -1, showing clearly its intercepts with the coordinate axes x+1 and the behaviour of the curve as it approaches its asymptotes 2/3
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