Question

Analyze the effect on the graph of f(x)=logx when f(x) is replaced by 5.9f(x) . For Response 1, enter 1 for compressed or 2 for stretched.(1 point) Compared to the graph of f(x) , the graph of 5.9f(x) has been vertically by a factor of

Answer 1

Given the function \( f(x) = \log x \), when it is replaced by \( 5.9f(x) \), we are transforming the original function to \( g(x) = 5.9 \log x \).

To analyze the effect of this transformation on the graph:

1. The term \( 5.9 \) is a vertical stretch factor. It means that each output value of the original function \( f(x) \) is multiplied by 5.9. Thus, for any input \( x \), the value of \( g(x) \) will be 5.9 times greater than \( f(x) \).

Therefore, the response for the compression or stretch analysis is:
- Since this transformation increases the output values rather than decreases them, it is a vertical stretch.

For Response 1, the answer is **2** for stretched.

2. In terms of the stretching factor, the graph of \( 5.9f(x) \) has been vertically stretched by a factor of 5.9 compared to the graph of \( f(x) \).

So in summary:

- Response 1: **2** (stretched)
- The graph of \( 5.9f(x) \) is vertically stretched by a factor of **5.9** compared to the graph of \( f(x) \).