Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with f(−x) + 4?

A) vertical reflection over x-axis and shifts up 4 units
B) vertical reflection over x-axis and shifts right 4 units
C) horizontal reflection over y-axis and shifts up 4 units
D) horizontal reflection over y-axis and shifts right 4 units

Answer 1

C) horizontal reflection over y-axis and shifts up 4 units

Explanation:

Given:

Parent function:

`f(x)=x`

Transformation:

`f(x)\rightarrow f(-x)+4`

Solution:

Transformation rules being applied.

`f(x)\rightarrow f(-x)`

Horizontal reflection on y-axis.

`f(x)\rightarrow f(x)+k`

Shift of
`k` units up.

Thus for the given transformation :
`f(x)\rightarrow f(-x)+4`

Transformation 1:
`f(x)\rightarrow f(-x)`

The above transformation carries out horizontal reflection on y-axis.

Transformation 2:
`f(x)\rightarrow f(-x)+4`

The above transformation will shift the graph 4 units up.

The effect on graph of
`f(x)` is horizontal reflection over y-axis and shifts up 4 units