Question 3 of 10 This q This Describe verbally the transformations that can be used to obtain the graph of $$ g $$ from the graph of $$ f $$. $$ g(x)=4^{x-1} ; f(x)=4^{x} $$ Select the correct choice below and, if necessary, fill in the answer box(es) within your choice. (Type integers or simplified fractions.) A. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) down. B. The graph of $$ g $$ is the graph of $$ f $$ shifted unit(s) up. C. The graph of $$ g $$ is the graph of $$ f $$ reflected in the $$ x $$-axis. D. The graph of g is the graph of f shifted $$ \square $$ unit(s) to the left. E. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) up and stretched horizontally by a factor of $$ \square $$ ] F. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) to the right and stretched horizontally by a factor of $$ \square $$ . G. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) to the left and stretched horizontally by a factor of $$ \square $$ . H. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) to the right. L. The graph of $$ g $$ is the graph of $$ f $$ shifted $$ \square $$ unit(s) down and stretched horizontally by a factor of $$ \square $$ . J. The graph of $$ g $$ is the graph of $$ f $$ reflected in the $$ y $$-axis.

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UpStudy AI · Accepted Answer

To obtain the graph of $$ g(x) = 4^{x-1} $$ from the graph of $$ f(x) = 4^{x} $$, you can analyze the transformation by comparing the two functions.

The function $$ g(x) = 4^{x-1} $$ can be rewritten as $$ g(x) = f(x-1) $$. This indicates a horizontal shift of the graph of $$ f(x) $$.

- **Horizontal Shift:** The term $$ x-1 $$ inside the function $$ f $$ means that the graph of $$ f $$ is shifted **1 unit to the right**.

There is no vertical shift, reflection, or stretching involved in this transformation.

**Correct Choice:**

**H. The graph of $$ g $$ is the graph of $$ f $$ shifted** $$ 1 $$ **unit(s) to the right.**
The graph of $$ g $$ is the graph of $$ f $$ shifted 1 unit to the right.

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