Question

Below is the graph of y = |x| . Translate it to make it the graph of y=|x+5|-3.

Answer 1

The function y = f(x - a) + b

is the horizontal translation of the function y = f(x) to the left (a is negative) or to the right (a is positive) by a units and

the vertical translation of the function y = f(x) up (b is positive) or down (b is negative) by b units

In this case,

`\begin{gathered} f(x)=|x| \\ a=-5 \\ b=-3 \end{gathered}`

Translate the parent function to the left by 5 units and

down by 3 units.

To make the graph y = |x + 5| - 3:

Translate the parent function

.