Question

if you vertically stretch the linear parent function f(x)=x, by a factor of 8, what is the equation of the new function

Answer 1

`g(x) = 8x`

Explanation:

Given:

`f(x) = x`

`Stretch\ factor = 8`

Required:

Equation of the new function.

Let the new function be represented by
`g(x)`

The interpretation of this question is that;

`g(x) = f(x * 8)`

Multiply 8 by x

`g(x) = f(8x)`

If

`f(x) = x`

then

`f(8x) = 8 * x`

Multiply 8 by x

`f(8x) = 8x`

Recall that

`g(x) = f(8x)`

Substitute
`f(8x) = 8x` in the above expression

`g(x) = 8x`

Hence, the equation of the new function when stretched by a factor of 8 is
`g(x) = 8x`