SAMPLE Test $1$

Name: $q,$ Date: $q,$

Please show all work. No credit will be given for the answer alone.

Given the graph of a function $y=f(x)$ find the following:

i$)\underset{x-5^{-}}{lim}f(x)=$

viii$)f(-2)=-1$

ii$)\underset{x-5^{+}}{lim}f(x)=-$

ix$)\underset{x{0}^{-}}{lim}f(x)=$

iii$)\underset{x-5}{lim}f(x)D$ N E

x$)\underset{x{0}^{+}}{lim}f(x)=4$

iv$)\underset{x-2^{-}}{lim}f(x)=3$

xi$)\underset{x}{lim}f(x)=-2$

v$)\underset{x-2^{+}}{lim}f(x)=-1$

xii$)\underset{x-}{lim}f(x)=0$

List the values of $x$ where $f(x)$ is discontinuous and explain why. Also list the horizontal and vertical asymptotes of $y=f(x).$

@$x=0$

$\underset{x{0}^{-}}{lim}f(x)=\underset{x{0}^{+}}{lim}f(x)$

$x=-5$

$(c)x=-2$

$\underset{x-2^{-}}{lim}f(x)\underset{x-2^{+}}{lim}f(x)$

$\underset{x5}{lim}f(x)\underset{?}{lim}f(x)$

$\underset{x-5^{-}}{lim},x-5^{+}$

and

$f(-5)is$

$ex=4$

Explain how one gets these answers with actual proof. Thank you