Answer the questions about the following function.

$f(x)=\frac{x+3}{x-11}$

$($a$)$ Is the point $(4,-\frac{4}{3})$ on the graph of $f?$

$($b$)$ If $x=1,$ what is $f(x)?$ What point is on the graph of $f?$

$($c$)$ If $f(x)=2,$ what is $x?$ What point$($s$)$ is $($are$)$ on the graph of $f?$

$($d$)$ What is the domain of $f?$

$($e$)$ List the $x-$intercepts, if any, of the graph of $f.$

$($f$)$ List the $y-$intercept, if there is one, of the graph of $f.$

$($g$)$ What are the zeros of $f?$

$($a$)$ Is the point $(4,-\frac{4}{3})$ on the graph of $f?$

A$.$ No$,$ because the domain of the function does not include $x=4.$

B$.$ No$,$ because the minimum of the function is larger than $-\frac{4}{3}.$

C$.$ Yes, the point is on the graph of $f.$

D$.$ No$,$ because when the function is evaluated for $x=4,$ the result is different than

$-\frac{4}{3}.$

$($b$)$ If $x=1,$ what is $f(x)?$

$f(1)=$

$($Type an integer or a simplified fraction.$)$

Using this information, list a point on the graph of $f.$

$($Simplify your answer. Type an ordered pair, using integers or fractions.$)$

$($c$).$ If $f(x)=2,$ what is $x?$

$x=$

$($Type an integer or a simplified fraction. Use a comma to separate answers as needed.$)$

Using this information, list a point on the graph of $f.$

$($Simplify your answer. Type an ordered pair, using integers or fractions.$)$

$($d$)$ What is the domain of $f?$

The domain is

$($Type your answer in interval notation.$)$