Question

What is the effect on the graph of the function f(x) = x when f(x) is replaced with -1/2 f(x)?

A) vertical reflection over x-axis and vertical stretch

B) vertical reflection over x-axis and vertical compression

C) horizontal reflection over y-axis and horizontal stretch

D) horizontal reflection over y-axis and horizontal compression

Answer 1

C) horizontal reflection over y-axis and horizontal stretch

Explanation:

1a- A vertical reflection over the x-axis occurs when a function
`f(x)` is transformed into
`f(-x)`

1b- A horizontal reflection over the y-axis occurs when a function
`f(x)` is transformed into
`-f(x)`

2a- A function is being compressed if
`f(x)` is multiplied by a positive factor k:
`k f(x)` with
`k>1`

2b- A function is being stretched if
`f(x)` is multiplied by a positive factor k:
`k f(x)` with
`k<1`

In our problem, the original function
`f(x)` is:

- Multiplied by 1/2, so by a factor which is smaller than 1, so we are in case 2b

- Transformed from
`f(x)` into
`-f(x)` (due to the negative sign in front of it), so we are in case 1b

So, overall, we had a horizontal reflection over the y-axis and a stretch of the function.