Question

The graph below have the same shape.what is the equation of the blue graph?

Answer 1

g(x) = (x - 5)²

Explanation:

This is an example of the transformation of functions.

In this example, we see the graph f(x) has been moved 5 in the positive direction on the x-axis.

Due to the fact that we are working with the x-axis, our transformation will be placed inside the bracket, and it will do the opposite of what we expect.

This means that our transformation will be set out in this format:

`g(x) = f(x-5)`

We know that:

`f(x) = x^2`

Therefore,

`g(x) = f(x-5) = (x-5)^2`

So,
`g(x) = (x-5)^2`.