Consider the following graphs with the given function formulas.

$($a$)(3$ points$)$ What is the domain of $q(x)?$ What is the range of $q(x)?$ Explain.

$($b$)(3$ points$)$ Use algebra to find the $x$ and $y$ intercepts of $h(t).$ Show work.

$($c$)(2$ points$)$ Find $h(q(4)).$ Show work.

$($d$)(2$ points$)$ For what intervals is $q(x)$ increasing? Decreasing? Explain.

$($e$)(2$ points$)$ For what intervals is $h(t)$ concave up$?$ Concave down? Explain.

$($f$)(3$ points$)$ For the function $q(x)$ find $A{V}_{[2,3]}.$ Show your work. Then, draw a line on the graph of $q(x)$ whose slope is this average rate of change.

$($g$)(3$ points$)$ What is $\underset{x}{lim}q(x)?$ What is $\underset{t}{lim}h(t)?$ Explain.

$($h$)(2$ points$)$ Does $q(x)$ have an inverse? Does $h(t)$ have an inverse? Explain.