Question

Which answer describes the transformation of f(x)=x2−1 to g(x)=(x−1)2−1 ?

a vertical translation 1 unit up

a horizontal translation 1 unit to the left

a vertical translation 1 unit down

a horizontal translation 1 unit to the right

Answer 1

a horizontal translation 1 unit to the right

f(x) x-intercept = 0.5
g(x) x-intercept = 0.5 + 1

Answer 2

The answer that describes the transformation f(x) tog(x) is:

a horizontal translation 1 unit to the right

Explanation:

We are given a parent function f(x) as:

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

and the transformed function g(x) is given by:

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

We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively.

Here we have: a= -1

This means that the shift is to the right by 1 units.

In other words we may say that the transformation is a horizontal translation 1 units to the right.