Question

Describe the transformation that takes f(x) =|x| to g(x)= -|x+4| -1

Please explain how you got your answer. Thanks!

Answer 1

First transformation:

f(x) is shifted left side by 4 units

Second transformation:

f(x) is shifted downward by 1 unit

Third transformation:

f(x) is reflected about x-axis

Explanation:

We are given

parent function as

`f(x)=|x|`

translated function is

`g(x)=-|x+4|-1`

First transformation:

We can see that there is x+4 in place of x

so, f(x) is shifted left side by 4 units

Second transformation:

1 is subtracted to y-value

so, f(x) is shifted downward by 1 unit

Third transformation:

-1 is multiplied to y-value

so, f(x) is reflected about x-axis