Question

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

1. a horizontal translation 1 unit to the left

2. a vertical translation 1 unit down

3. a horizontal translation 1 unit to the right

4. a vertical translation 1 unit up

Answer 1

The correct answer is 3. A horizontal translation 1 unit to the right.

Explanation:

In the transformation from f(x) = x^2 - 1 to g(x) = (x - 1)^2 - 1, the function has been horizontally translated 1 unit to the right. This is because the x value in the original function f(x) has been replaced with (x - 1) in g(x), which means that the graph of g(x) will be shifted 1 unit to the right compared to the graph of f(x).

Answer 2

the answer is the third choice ( a horizontal translation 1 unit to the right )