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

Answer:

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

Step-by-step 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)