EXPLANATION:
Given;
We are given the function below;
[tex]f(x)=3^x[/tex]
Required;
We are required to describe what change would be made to graph the function;
[tex]g(x)=3^{x-7}[/tex]
For a function given such as the one here, when the graph is shifted to the right, then the original function is affected as follows;
[tex]\begin{gathered} f(x)=x \\ \\ Shift\text{ }to\text{ }the\text{ }right: \\ f(x)+(x)=x \\ \\ Subtract\text{ }(x)\text{ }from\text{ }both\text{ }sides: \\ f(x)+(x)-(x)=x-(x) \\ \\ f(x)=x-(x) \end{gathered}[/tex]
For a shift to the left, we would have a plus sign, that is, add x number of units the graph is being shifted.
Therefore, for a function that has changed such as the one given,
[tex]g(x)=3^{x-7}[/tex]
What we have is shift the original graph 7 units to the right.
ANSWER:
[tex]Shift\text{ }the\text{ }graph\text{ }7\text{ }units\text{ }right[/tex]
The first option is the correct answer.
