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 horizontal compression 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 vertical stretch 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 vertical compression of the graph of $f(x)$.

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

c) Assume $b>1$ 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. $g(x)=f(2x)$) for the following:
i) The graph of $g(x)=$ is the graph of $f(x)$ horizontally stretched by a factor of $b$.
ii) The graph of $g(x)=$ is the graph of $f(x)$ horizontally compressed by a factor of $b$.

Hint: