Question

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

A) shifts down 1 unit
B) shifts left 1 unit
C) vertical reflection over x-axis
D) horizontal reflection over y-axis

Answer 1

C) vertical reflection over x-axis

Explanation:

Given function
`f(x)=x`

And
`f(x)` being replaced with
`-f(x)`

Here
`x` is input and
`f(x)` is the output.

If we multiply
`-1` to all outputs that is
`f(x)`. It will results in
`-f(x)`. Also, the new output
`-f(x)` will give reflection of the
`f(x)` vertoically over X-axis.

As given function
`f(x)`, then function
`-f(x)` will be a vertical reflection about the X-axis.