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

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theleangreenbean

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.

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