Question

Consider the function f(x). Select all of the following that include a vertical stretch of f(x)

A. -2f(x)
B. 0.25f(x)
C. -f(x) + 6
D. 5.5f(x) - 1
E. f(x) + 9
F. 7f(x)

Answer 1

A, D and F.

Explanation:

If f(x) is a function and another function is defined as

`g(x)=kf(x)`

If |k|>1, then it is clear vertical stretch.

If 0<|k|<1, then it is clear vertical compression.

In function
`-2f(x)`,

`|k|=|-2|=2>1` vertical stretch.

In function
`0.25f(x)`,

`|k|=|0.25|=0.25<1` vertical compression.

In function
`-f(x)+6`,

`|k|=|-1|=1` neither stretch nor compression.

In function
`5.5f(x)-1`,

`|k|=|5.5|=5.5>1` vertical stretch.

In function
`f(x)+9`,

`|k|=|1|=1` neither stretch nor compression.

In function
`7f(x)`,

`|k|=|7|=7>1` vertical stretch.

Hence, the correct options are A, D and F.

Answer 2

F , D, A

Explanation:

As we know vertical stretch of f(x) happens when we chane the value of the patameter a in this general form:

y = a. f(k(x-d))+ c

when |a| > 1 because When |a| > 1 (when a is greater than 1), the function is stretched vertically by a dilation factor of |a|.

So we choose, F , D, A