Stretching graphs

What is a stretch?

A stretch is when we change the shape of a graph by making it taller/shorter (vertical stretch) or wider/thinner (horizontal stretch).

Equation of a stretched function

\frac ya=f(\frac xb)

Where:

• a is the vertical stretch factor
• b is the horizontal stretch factor

Example: find the equation of the function f(x) stretched vertically by a factor of 3 and horizontally by a factor of 2.

• a=3
• b=2
• \frac ya=f(\frac xb)
• \frac y3=f(\frac x2)
• y=3f(\frac x2)

Example: find the equation of the function f(x) compressed vertically by a factor of \frac34 and stretched horizontally by a factor of \frac12.

• a=\frac34
• b=\frac12
• \frac ya=f(\frac xb)
• \frac y{\frac34}=f(\frac x{\frac12})
• y=\frac34f(2x)

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