# Transformations of functions: Vertical stretches

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##### Intros
###### Lessons
1. An Experiment to Study "Vertical Stretches"
Sketch and compare: $\left( y \right) = {x^2} + 2$
VS.
$\left( {2y} \right) = {x^2} + 2$
VS.
$\left( {\frac{y}{3}} \right) = {x^2} + 2$
2. a) Sketch all three quadratic functions on the same set of coordinate axes.
3. 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
1. Vertical Stretches
Given the graph of $y = f\left( x \right)$ as shown, sketch:
1. $y = \frac{1}{2}f\left( x \right)$
2. $y = \frac{4}{3}f\left( x \right)$
3. 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 ______________________.