Question

What is the horizontal and vertical shift for the absolute value function below f(x)=3[x+9]+6

Answer 1

We will see that we have a shift of 9 units to the left and 6 units upwards

How to identify the translations?

For any given function H(x), we define a vertical shift of N units as:

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

• If N > 0, the shift is upwards.
• If N < 0, the shift is downwards.

While a horizontal shift is written as:

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

• If N > 0, the shift is to the left.
• if N < 0, the shift is to the right.

Here we know that:

f(x) = 3*|x + 9| + 6

If the original function was:

H(x) = 3*|x|

Then we can write:

f(x) = H(x + 9) + 6

So we have a shift of 9 units to the left and 6 units upwards.

If you want to learn more about translations:

brainly.com/question/24850937

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