Question

What is the vertical shift for the absolute value function below. Explain how you know using complete sentences. Include the direction and number of units of the shift. f(x)=9|x+1|+2

Answer 1

The vertical shift of the function $f(x) = 9|x + 1| + 2$ is 2 units up

The absolute function is given as:

$f(x) = 9|x + 1| + 2$

An absolute function is represented as:

$f(x) = a|x - h| + k$

Where k represents the vertical shift.

By comparison, the value of k is:

$k = 2$

This means that the vertical shift is 2 units

Hence, the vertical shift of the function $f(x) = 9|x + 1| + 2$ is 2 units up

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