Question

The function g(x) undergoes a reflection over the x-axis, a horizontal shift left 4 units, and a vertical shift down 2 units to become f(x).
Which equations describes f(x)?

a. f(x)=|−x+4|−2
b. f(x)=|−x−4|−2
c. f(x)=−|x+4|−2
d. f(x)=−|x−4|−2
please only answer if you know correct answer, I will give brainliest.

Answer 1

Answer: Choice C

f(x) = -|x+4|-2

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Explanation:

The parent function is g(x) = |x| which is the absolute value function.

Reflect it over the y axis to get -|x|

Replace x with x+4 to shift the graph 4 units to the left. So we have -|x+4|

Lastly, tack on a -2 at the end to shift 2 units down

We'll end up with f(x) = -|x+4|-2 which is choice C.

The sequence of graphs, showing the step by step transformation process, is shown below.