Answer:
Option: C is the correct answer.
C. y=|x+4|-2
Step-by-step explanation:
We know that the vertex of a absolute value function or a modulus function f(x) of the type:
f(x)=a|x-h|+k
is denoted by V such that:
V=(h,k)
By looking at the graph of the function we see that the vertex of the function is:
(-4,-2)
A)
y=|x+4|+2
The vertex of this function is:
(-4,2)
Hence, option: A is incorrect.
B)
y=|x-4|+2
The vertex of this function is: (4,-2).
Hence, option: B is incorrect.
D)
y=|x-4|-2
The vertex of this modulus function is: (4,-2)
Hence, option: D is incorrect.
C)
y=|x+4|-2
The vertex of this function is: (-4,-2)
Also, we see that the graph of this function matches the given graph.
Hence, option: C is correct.
