14.5 Horizontal stretches in transformations
Horizontal stretches in transformations
Lessons

a)
Sketch the following functions on the same set of coordinate axes:
$y = {\left( {x  4} \right)^2}$ $y = {\left( {2x  4} \right)^2}$ $y = {\left( {\frac{x}{3}  4} \right)^2}$ 
b)
Compared to the graph of $y = {\left( {x  4} \right)^2}$:
• $y = {\left( {2x  4} \right)^2}$ is a horizontal stretch about the yaxis by a factor of _____________.
• $y = {\left( {\frac{x}{3}  4} \right)^2}$ is a horizontal stretch about the yaxis by a factor of _____________.


a)
$y = f\left( {2x} \right)$

b)
$y = f\left( {\frac{1}{3}x} \right)$

c)
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 ______________________.
