Video: Transformations of Functions

The function 𝑦 = 𝑓(π‘₯) is stretched in the vertical direction by a scale factor of 1/2. Write, in terms of 𝑓(π‘₯), the equation of the transformed function.

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Video Transcript

The function 𝑦 equals 𝑓 of π‘₯ is stretched in the vertical direction by a scale factor of one-half. Write in terms of 𝑓 of π‘₯ the equation of the transformed function.

The function we’re working with is 𝑦 equals 𝑓 of π‘₯. And it’s being stretched with a scale factor of one-half. When we use a scale factor with a function, we multiply every part of the function by our scale factor. Here’s what I mean.

If, for example, we have the function 𝑦 equals four π‘₯ plus two and we wanted to use the scale factor of one-half, we would multiply every term in our function by one-half: one-half times four π‘₯ plus two.

Distributing the one half across both terms, four times one half equals two π‘₯. One-half times two equals one.

We would follow the same process for 𝑓 of π‘₯. One-half times 𝑓 of π‘₯. 𝑦 equals the function of π‘₯ over two. Multiplying 𝑓 of π‘₯ by one-half is the same thing as saying the function of π‘₯ divided by two.

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