Question

How do I find the stretches of a transformed function?

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

Answer 1

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.