3x+2 The function f is defined by f(x) = for xe R, xp, xq. 4x²-1 (a) Find the value of p and the value of q. (b) Find an expression for f'(x). The graph of y = f(x) has exactly one point of inflexion. (c) Find the x-coordinate of the point of inflexion. (d) Sketch the graph of y = f(x) for -3≤x≤3, showing the values of any axes intercepts, the coordinates of any local maxima and local minima, and giving the equations of any asymptotes. 4x²-1 2 The function g is defined by g(x): 9 for xeR, x 3x+2 3 (e) Find the equations of all the asymptotes on the graph of y = g(x). (f) By considering the graph of y = g(x) - f (x), or otherwise, solve f(x)
3x+2 The function f is defined by f(x) = for xe R, xp, xq. 4x²-1 (a) Find the value of p and the value of q. (b) Find an expression for f'(x). The graph of y = f(x) has exactly one point of inflexion. (c) Find the x-coordinate of the point of inflexion. (d) Sketch the graph of y = f(x) for -3≤x≤3, showing the values of any axes intercepts, the coordinates of any local maxima and local minima, and giving the equations of any asymptotes. 4x²-1 2 The function g is defined by g(x): 9 for xeR, x 3x+2 3 (e) Find the equations of all the asymptotes on the graph of y = g(x). (f) By considering the graph of y = g(x) - f (x), or otherwise, solve f(x)
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter8: Functions
Section8.4: More Quadratic Functions And Applications
Problem 55PS
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Transcribed Image Text:3x+2
The function f is defined by f(x) =
for xe R, xp, xq.
4x²-1
(a) Find the value of p and the value of q.
(b) Find an expression for f'(x).
The graph of y = f(x) has exactly one point of inflexion.
(c)
Find the x-coordinate of the point of inflexion.
(d) Sketch the graph of y = f(x) for -3≤x≤3, showing the values of any axes intercepts,
the coordinates of any local maxima and local minima, and giving the equations of
any asymptotes.
Transcribed Image Text:4x²-1
2
The function g is defined by g(x):
9
for xeR, x
3x+2
3
(e)
Find the equations of all the asymptotes on the graph of y = g(x).
(f)
By considering the graph of y = g(x) - f (x), or otherwise, solve f(x) <g(x) for x = R.
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