# Transformations of functions: Horizontal stretches

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##### Intros

###### Lessons

__An Experiment to Study "Horizontal Stretches"__

Sketch and compare: $y = {\left( {x - 4} \right)^2}$ VS. $y = {\left( {2x - 4} \right)^2}$ VS. $y = {\left( {\frac{x}{3} - 4} \right)^2}$- Sketch all three quadratic functions on the same set of coordinate axes.
- Compared to the graph of $y = {\left( {x - 4} \right)^2}$:

• $y = {\left( {2x - 4} \right)^2}$ is a horizontal stretch about the y-axis by a factor of _____________.

• $y = {\left( {\frac{x}{3} - 4} \right)^2}$ is a horizontal stretch about the y-axis by a factor of _____________.

##### Examples

###### Lessons

**Horizontal Stretches**

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

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

• $\left( x \right) \to \left( {\frac{1}{3}x} \right)$: horizontal stretch by a factor of ________ ⇒ all $x$ coordinates ______________________.