We will find the correct answer by elimination.
From the graph, we see that function takes the following values:
0. for x = 1, g(1) = -4,
,
1. for x = 5, g(5) = 4.
A) We evaluate the function from point A at x = 1, we get:
[tex]g(1)=-3\cdot1-5=-8\ne-4\text{ }✖[/tex]
So option A is not the answer.
B) We evaluate the function from point B at x = 1, we get:
[tex]g(1)=-2\cdot1+2=0\ne-4\text{ }✖[/tex]
So option B is not the answer.
D) We evaluate the function from point D at x = 5, we get:
[tex]g(5)=-3\cdot5+16=-15+16=1\ne4\text{ }✖[/tex]
So option D is not the answer.
Because the functions from options A, B and D don't describe the curve of the graph, the option left is option C.
Answer: C
