# Transformations of functions: Vertical stretches

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##### Intros

###### Lessons

**An Experiment to Study "Vertical Stretches"**

Sketch and compare: $\left( y \right) = {x^2} + 2$ VS. $\left( {2y} \right) = {x^2} + 2$ VS. $\left( {\frac{y}{3}} \right) = {x^2} + 2$- a) Sketch all three quadratic functions on the same set of coordinate axes.
- Compared to the graph of $\left( y \right) = {x^2} + 2$:

• $\left( {2y} \right) = {x^2} + 2$ is a vertical stretch about the x-axis by a factor of ____________.

• $\left( {\frac{y}{3}} \right) = {x^2} + 2$ is a vertical stretch about the x-axis by a factor of ____________.

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##### Examples

###### Lessons

**Vertical Stretches**

Given the graph of $y = f\left( x \right)$ as shown, sketch:- $y = \frac{1}{2}f\left( x \right)$
- $y = \frac{4}{3}f\left( x \right)$
- In conclusion:

• $\left( y \right) \to \left( {2y} \right)$: vertical stretch by a factor of ________ ⇒ all $y$ coordinates ______________________.

• $\left( y \right) \to \left( {\frac{3}{4}y} \right)$: vertical stretch by a factor of ________ ⇒ all $y$ coordinates ______________________.