Question

How would the graph of the function y=|x|-4 be affected if the function were changed to y=|x|-1?

Answer 1

`y =|x| - 4` is translated 3 units up

Explanation:

Given

`y =|x| - 4`

Required

The changes that makes it to:
`y =|x| - 1`

By observation, we can see that
`y =|x| - 4` was translated up to
`y =|x| - 1`

Next, is to calculate the units of translation (c)

Represent the old function as:

`y=\left|x\right|-4 + c`

Equate y and y

`\left|x\right|-4 + c =\left|x\right|-1`

Cancel out |x|

`-4 + c=-1`

Solve for c

`c = 4 - 1`

`c = 3`