Question

If you horizontally stretch the quadratic parent function, f(x)= x^2, by a factor of 4, what is the equation of the new function

Answer 1

`f(x) = (1)/(16)x^2`

Explanation:

If the graph of the function
`y=f(hx)` represents the transformations made to the graph of
`y= f(x)` then, by definition:

If
`0 <h <1` the graph is stretched horizontally by a factor
`(1)/(h)`

If
`h> 1` the graph is compressed horizontally by a factor
`(1)/(h)`

In this problem we have the parent function
`y=x^2` And we know that it stretches horizontally by a factor of 4

Therefore

`0 <h <1` and
`h=(1)/(4)`

The transformation is:

`y=f((1)/(4)x)`

And the function is:

`f(x) = ((1)/(4)x)^2`