Question

True or false? multiplying the parent linear function by 3/4 results in vertical stretch

Answer 1

Transformations of Functions

f(x) ⇒ a*f(x)

This results in a vertical stretch, or compression.

• When a > 1, we refer to this as a vertical stretch by a factor of a.
• When 0 < a < 1, we typically refer to this as a vertical compression by a factor of
  `(1)/(a)`.*

*There are multiple correct answers when asked about a, or vertical stretches/compressions.

• Let's say we're given
  `(1)/(2)f(x)`. In this case, 0 < a < 1.

We could say the following:

• f(x) underwent a vertical stretch by a factor of
  `(1)/(2)`.
• f(x) underwent a vertical compression by a factor of 2.

Both of the above responses are correct.

Solving the Question

We're given:

• We multiply the parent function by
  `(3)/(4)`.

In this case, 0 < a < 1.

• This results in a vertical stretch by a factor of
  `(3)/(4)`.
• This results in a vertical compression by a factor of
  `(4)/(3)`.

Answer

True and false. Yes, we did modify the vertical stretch factor of the function to induce a type of vertical stretch. No, it is not a vertical stretch per se, but it is rather a vertical compression.