Exercise 7 Page 6

The given function is an absolute value function, so its parent function is $f (x) = ∣ x ∣ .$ We will start by graphing both functions in one coordinate plan. Then we will compare them to describe the transformation.

Graphing the Functions

To graph both of the functions, we will use the table of values. We will choose a variety of $x -$ values: at least one negative, $0,$ and at least one positive.

$x$	$f (x) = ∣ x ∣$	$c (x) = 0.2 ∣ x ∣$
$- 5$	$∣ - 5 ∣ = 5$	$0.2 ∣ - 5 ∣ = 1$
$0$	$∣ 0 ∣ = 0$	$0.2 ∣ 0 ∣ = 0$
$5$	$∣ 5 ∣ = 5$	$0.2 ∣ 5 ∣ = 1$

Now let's plot the functions using these points! Remember that the graph of absolute value functions is V-shaped.

Comparing the Functions

Having drawn our functions, we can describe the transformation.

We see that each $y -$ value is being multiplied by $0.2$ and all points are being pushed towards the $x -$ axis. This is a vertical shrink by a factor of $0.2 .$