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Let $f(x)=x^2-1$ , $g(x)=2f(x)=2(x^2-1)$ , and $h(x)=.5f(x)=.5(x^2-1)$ . Fill in the following table:

$x$	-2	-1	0	1	2
$f(x)$
$g(x)$
$h(x)$

The following are graphs of the functions $f(x)$ , $g(x)$ , and $h(x)$ .

a) Which of the following statements best describes the differences between the graphs of $f(x)$ and $g(x)$ ?

A. The graph of $g(x)$ is a vertical stretch of the graph of $f(x)$ .

B. The graph of $g(x)$ is a vertical compression of the graph of $f(x)$ .

C. The graph of $g(x)$ is a horizontal stretch of the graph of $f(x)$ .

D. The graph of $g(x)$ is a horizontal compression of the graph of $f(x)$ .

b) Which of the following statements best describes the differences between the graphs of $f(x)$ and $h(x)$ ?

A. The graph of $g(x)$ is a vertical stretch of the graph of $f(x)$ .

B. The graph of $g(x)$ is a horizontal compression of the graph of $f(x)$ .

C. The graph of $g(x)$ is a horizontal stretch of the graph of $f(x)$ .

D. The graph of $g(x)$ is a vertical compression of the graph of $f(x)$ .

c) Assume $a>1$ and $f(x)$ is a function. Based on your work above, try to write an implicit formula (a function in terms of $f(x)$ , e.g. $g(x)=2f(x)$ ) for the following:
i) The graph of $g(x)=$ is the graph of $f(x)$ vertically stretched by a factor of $a$ .
The graph of $g(x)=$ is the graph of $f(x)$ vertically compressed by a factor of $a$ .

Hint: