Answer:
The correct option is D.
Step-by-step explanation:
From the given graph it is clear that the y-intercept of the function is -1. It means the graph passes through (0,-1).
Check each function, whether the function passes through the point (0,-1) or not. Substitute x=0 it each function to find the y-intercept.
In option A,
[tex]g(x)=|x|[/tex]
[tex]g(0)=|0|=0[/tex]
The y-intercept of the function is at (0,0).
In option B,
[tex]g(x)=x^2[/tex]
[tex]g(0)=0^2=0[/tex]
The y-intercept of the function is at (0,0).
In option C,
[tex]g(x)=x[/tex]
[tex]g(0)=0[/tex]
The y-intercept of the function is at (0,0).
In option D,
[tex]g(x)=-2^x[/tex]
[tex]g(0)=-1[/tex]
The y-intercept of the function is at (0,-1).
The graph of [tex]g(x)=-2^x[/tex] passes through the point (0,-1).
Therefore the correct option is D.
