# Video: Transformations of Functions

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

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### Video Transcript

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

The function weβre working with is π¦ equals π of π₯. And itβ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. Hereβs what I mean.

If, for example, we have the function π¦ 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 π of π₯. One-half times π of π₯. π¦ equals the function of π₯ over two. Multiplying π of π₯ by one-half is the same thing as saying the function of π₯ divided by two.