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

Answer:

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.