What is a vertical stretch of a function

Now Playing:Transformations of functions vertical stretches– Example 1

An Experiment to Study "Vertical Stretches"
Sketch and compare: $\left( y \right) = {x^2} + 2$
VS.
$\left( {2y} \right) = {x^2} + 2$
VS.
$\left( {\frac{y}{3}} \right) = {x^2} + 2$
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.
An Experiment to Study "Vertical Stretches"
Sketch and compare: $\left( y \right) = {x^2} + 2$
VS.
$\left( {2y} \right) = {x^2} + 2$
VS.
$\left( {\frac{y}{3}} \right) = {x^2} + 2$
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 ____________.

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 ______________________.