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

User NightElfik
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1 Answer

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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.

User Ronnie Overby
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