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

Answer:

The correct answer is a horizontal translation 1 unit to the right

Step-by-step explanation:

Answer 2

By describing the general translations, we will see that g(x) is a translation of one unit to the right of f(x).

How to identify a transformation?

Here we have the transformation from:

f(x) = x^2 - 1

to:

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

Now we know that this is a translation, there are two types of translations.

Vertical translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N.

• If N is positive the translation is upwards.
• If N is negative, the translation is downwards.

Horizontal translation:

For a function f(x), a vertical translation of N units is written as:

g(x) = f(x + N).

• If N is positive the translation is to the left.

• If N is negative the translation is to the right.

In this case, we can see that:

f(x) = x^2 - 1

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

Then we can see that we have a translation of 1 unit to the right.

If you want to learn more about translations, you can read:

https://brainly.com/question/17586310