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 [tex]\dfrac{1}{a}[/tex].*
*There are multiple correct answers when asked about a, or vertical stretches/compressions.
- Let's say we're given [tex]\dfrac{1}{2}f(x)[/tex]. In this case, 0 < a < 1.
We could say the following:
- f(x) underwent a vertical stretch by a factor of [tex]\dfrac{1}{2}[/tex].
- 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 [tex]\dfrac{3}{4}[/tex].
In this case, 0 < a < 1.
- This results in a vertical stretch by a factor of [tex]\dfrac{3}{4}[/tex].
- This results in a vertical compression by a factor of [tex]\dfrac{4}{3}[/tex].
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.
