# Video: Transformations of Functions

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

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### Video Transcript

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

The function we’re working with is 𝑦 equals 𝑓 of 𝑥. 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 𝑥 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 𝑥 plus two.

Distributing the one half across both terms, four times one half equals two 𝑥. One-half times two equals one.

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