Answer:
C. [tex]g(x)=2^{x}+1[/tex]
Step-by-step explanation:
We know that the parent function is [tex]y=2^{x}[/tex].
Now, the function that the graph shows intercepts [tex]y=-1[/tex], and the problem states that is the reflection of [tex]g(x)[/tex] across the x-axis. That means the original function has to intercept [tex]y=1[/tex], which is the reflected interception of [tex]y=-1[/tex].
We also know that y-interceptions are shown as independent terms, so the function [tex]g(x)[/tex] is defined as follows
[tex]g(x)=2^{x}+1[/tex]
Where [tex]+1[/tex] represent the y-interception.
The graph of [tex]g(x)[/tex] is attached. The red curve represents [tex]g(x)[/tex] and the blue curve represents [tex]f(x)[/tex]. You can observe that models exactly the function we are looking for.
