The functions f(x) and g(x) are shown on the graph.
f(x)=|x|

What is g(x)

Option B

Step-by-step explanation:

As shown in the picture, g(x) is the red one which can be obtained by translating f(x) - the blue one toward +x-axis direction 4 units.

=> g(x) = f(x) + 4 = |x| + 4

Choice D

g(x) = |x-4|

Explanation:

Replacing x with x-4 shifts the xy axis four units to the left. If we fix the blue V shape to not move while the xy axis does move, then it gives the illusion of the V shape moving 4 units to the right to end up producing the red curve.

You can use a table of values to compare the two functions or you could use a graphing tool to confirm the answer.

Extra info:

Choice A will move the blue graph 4 units down

Choice B will move the blue graph 4 units up

Choice C will move the blue graph 4 units to the left