What is a horizontal stretch of a function

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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 _____________.

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Horizontal Stretches
Given the graph of $y = f\left( x \right)$ $y = f (x)$ as shown, sketch:
1. $y = f\left( {2x} \right)$
2. $y = f\left( {\frac{1}{3}x} \right)$
3. 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 ______________________.

Transformations of functions: Horizontal stretches