Exercise 41 Page 382

We are first asked to complete the table for the function $y=\frac{x+4}{x^2-16}.$ Let's plug in the given values of $x$ to compute our values.

Complete the Table

We will start with $x=\text{-}3.5.$ Let's substitute the rest of our values into the function in order to fill out the table.

$x$	$y=\frac{x+4}{x^2-16}$
$\text{-}3.5$	$\text{-}0.1333$
$\text{-}3.8$	$\text{-}0.1282$
$\text{-}3.9$	$\text{-}0.1266$
$\text{-}4.1$	$\text{-}0.1235$
$\text{-}4.2$	$\text{-}0.1220$

Behavior at $x=\text{-}4$

To draw the graph using a calculator, we first press $\boxed{\text{Y=}}$ and type the function in one of the available rows. Having written the function, we can push the $\boxed{\text{GRAPH}}$ button to see an image of it.

We want to evaluate the behavior of the function at $x=\text{-}4.$ Let's resize the window by pushing $\boxed{\text{WINDOW}}$ and changing the minimum and maximum of our axes.

To find the value at $x=\text{-}4$, push $\boxed{2\text{nd}},$ $\boxed{\text{TRACE}},$ and then choose the first option, value. Next, type in the value $x=\text{-}4.$

We see the graph does not have a value for $y$ when $x=\text{-}4.$ This is because if we plug in the value $x=\text{-}4$ into our function, the function is undefined. Let's plug in the values $x=\text{-}3.9999$ and $x=4.0001$ to see the $y\text{-}$ value it approaches.

We see that our graph approaches $y=\text{-}0.125.$