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Chapter 0: Problem 7
Find \(a\) if the line passing through \((1,3)\) and \((-4, a)\) has slope 5.
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Sketch the graph of the first function by plotting points if necessary. Then use transformation(s) to obtain the graph of the second function. $$y=x^{2}, \quad y=\left|x^{2}-2 x-1\right|$$ 54\. $$y=\tan x, \quad y=\tan \left(x+\frac{\pi}{3}\ri
The graph of the function \(f\) is to be transformed as described. Find the function for the transformed graph. \(f(x)=\sqrt{x}+1\); shifted horizontally to the left by 1 unit, compressed horizontally by a factor of 3, stretched vertically by a factor of 3, and shifted vertically downward by 2 units
Determine whether \(h=g \circ f\) is even, odd, or neither, given that a. both \(g\) and \(f\) are even. b. \(g\) is even and \(f\) is odd. c. \(g\) is odd and \(f\) is even. d. both \(g\) and \(f\) are odd.
You are given the graph of a function \(f .\) Determine whether \(f\) is one-to- one.
Find the inverse of \(f .\) Then sketch the graphs of \(f\) and \(f^{-1}\) on the same set of axes. $$ f(x)=\sin (2 x-1), \quad \frac{1}{2}\left(1-\frac{\pi}{2}\right) \leq x \leq \frac{1}{2}\left(1+\frac{\pi}{2}\right) $$
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