Answer:
c. the graph is not shifted horizontally from the graph of f(x)
Step-by-step explanation:
The parent function is given by ![f(x)=2^x](https://tex.z-dn.net/?f=f%28x%29%3D2%5Ex)
The transformation function is ![g(x)=f(x)+k](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29%2Bk)
For k = -5, we have
![g(x)=f(x)-5\\\\g(x)=2^x-5](https://tex.z-dn.net/?f=g%28x%29%3Df%28x%29-5%5C%5C%5C%5Cg%28x%29%3D2%5Ex-5)
The transformation of graph rule: Whenever, we add or subtract any constant in the function then there will be transformation in vertical direction.
- If we add a constant k to the function then the graph of the function will shift up by k units.
- If we subtract a constant k to the function then the graph of the function will shift down by k units.
Whenever, we add/subtract any constant in the x values then there would be transformation in horizontal direction.
Here 5 is subtracted in f(x) to get g(x) hence, here will be transformation in vertical direction not in horizontal direction.
Therefore, c is the correct option.
c. the graph is not shifted horizontally from the graph of f(x)