Question

Let f(x)=x. The graph of f(x) ​is transformed into the graph of g(x) by a vertical stretch of 4 units and a translation of 4 units up.

What is the equation for g(x) ?

Answer 1

g(x) = 4x + 4.

Explanation:

f(x) = x

Vertical stretch gives 4x.

A translation of 4 up gives 4x + 4.

Answer 2

`g(x) = 4x + 4`

Explanation:

The given function is f(x)=x.

If we stretch vertically by a factor of 4 and a translation of 4 units up then the new function becomes

`g(x) = 4f(x) + 4`

But f(x)=x

We substitute to obtain the equation of g(x) as

`g(x) = 4x + 4`