Question

Identify a transformation of the function ƒ(x) = x^2 by observing the equation of the function g(x) = (x – 1)^2

Answer 1

f(x) is translated 1 units left to give g(x)

Explanation:

Given

`f(x) = x^2`

`g(x) = (x - 1)^2`

Required

How does f(x) transform to g(x)

`f(x) = x^2`

When translated by b units left, it gives:

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

In this case:

`b = 1`

So:

`g(x) = f(x - 1)`

If
`f(x) = x^2`, then

`f(x - 1) = (x - 1)^2`

Hence:

`g(x) = (x - 1)^2`

This implies that; f(x) is translated 1 units left to give g(x)