How do I find the stretches of a transformed function?

Do I look for the x and y intercepts and the invariant points?

1 Answer
Feb 9, 2018

Look at the variables of a and b to figure out what factor to stretch by.

Explanation:

Refer to: y=af(b(x-h))+k

A vertical stretch is the stretching of a function on the x-axis.
If |a|>1, then the graph is stretched vertically by a factor of a units.
If the values of a are negative, this will result in the graph reflecting vertically across the x-axis.

A horizontal stretch is the stretching of a function on the y-axis.
If |b|<1, then the graph is stretched horizontally by a factor of b units.
If the values of b are negative, this will result in the graph reflecting horizontally across the y-axis.

For example:
y=2f((1/2)x-h))+k
a=2

b=1/2

To vertically stretch we use this formula:
y^1=ay
y^1=2y So, the vertical stretch would be by a factor of 2.

To horizontally stretch we use this formula:
x^1=x/b

x^1=x/(1/2)

x^1=2x So, the horizontal stretch would be by a factor of 2 as well.

Extras:
If |a|<1, this results in a vertical compression.
If |b|>1, this results in a horizontal compression.