Let's solve the given problem step-by-step.
We are given the function [tex]\(93 f(x)\)[/tex] and we want to determine how the graph of this function is related to the graph of the original function [tex]\(f(x)\)[/tex].
### Step 1: Understanding Scaling Factors
When we modify a function by multiplying it by a constant, it affects the graph of the function in a specific way:
- If we multiply the function [tex]\(f(x)\)[/tex] by a constant [tex]\(k\)[/tex]:
- If [tex]\(k > 1\)[/tex], the graph of the function is vertically stretched.
- If [tex]\(0 < k < 1\)[/tex], the graph of the function is vertically compressed.
- If [tex]\(k < 0\)[/tex], the graph is also reflected over the x-axis and then stretched or compressed depending on the magnitude of [tex]\(k\)[/tex].
### Step 2: Application to Our Function
In our case, the constant we are multiplying the function by is 93, which is greater than 1. Therefore:
- The function [tex]\(93 f(x)\)[/tex] is obtained by vertically stretching the graph of [tex]\(f(x)\)[/tex] by a factor of 93.
### Step 3: Evaluating the Options
Given the multiple-choice options:
- Horizontally stretching the graph of [tex]\(f(x)\)[/tex] by a factor of 93
- Horizontally compressing the graph of [tex]\(f(x)\)[/tex] by a factor of 93
- Vertically stretching the graph of [tex]\(f(x)\)[/tex] by a factor of 93
- Vertically compressing the graph of [tex]\(f(x)\)[/tex] by a factor of 93
The correct option is:
- Vertically stretching the graph of [tex]\(f(x)\)[/tex] by a factor of 93
### Conclusion
Therefore, the graph of the function [tex]\(93 f(x)\)[/tex] can be obtained from the graph of [tex]\(y = f(x)\)[/tex] by vertically stretching the graph of [tex]\(f(x)\)[/tex] by a factor of 93.
