b Let's compare the graph of the ball's path to the parent absolute value function. First, we need to graph them on the same coordinate plane.

How can we write a transformation of the parent function such that the new function will be the same as the ball's path? The slopes are the same for both functions, so we know that it will only be translations. So, how can we get from the parent vertex to the transformed vertex?

The graph is shifted by

1

unit up, a vertical translation, and

7

units to the right, a horizontal translation. Let's write the general form for a vertical and a horizontal translation.

Vertical translation : Horizontal translation : g (x) = f (x) + k g (x) = f (x - h)

In this form,

k

is the number of units the graph is shifted up (for positive numbers) or down (for negative numbers), and

h

is the number of units the graph is shifted right (for positive numbers) or left (for negative numbers). The graph of the function is shifted

1

unit up and

7

units to the right. Let's write the equation for the transformation.

y = ∣ x - 7 ∣ + 1

Exercise