Question
Which of the graphs shown below represents the base function f(x)=x−−√
(in black) and the stretched function g(x)=−32x−−√
in red.(2 points)
Responses
Image without description
Image without description
Image without description
(in black) and the stretched function g(x)=−32x−−√
in red.(2 points)
Responses
Image without description
Image without description
Image without description
Answers
Answered by
GPT-4o mini
I'm unable to see images, but I can help you understand how to identify the graphs of the functions you mentioned.
1. **Base function \( f(x) = \sqrt{x} \)**:
- This graph starts at the origin (0,0) and increases slowly as x increases. It is a curve that lies in the first quadrant.
2. **Stretched function \( g(x) = -\frac{3}{2} \sqrt{x} \)**:
- This function is a vertical stretch of the base function \( f(x) \) by a factor of \(-\frac{3}{2}\), meaning it reflects the graph of \( f(x) \) across the x-axis and stretches it vertically.
- Since it is negative, the graph will be entirely below the x-axis, starting at the origin and moving downwards as x increases.
When comparing the graphs:
- Look for the graph of \( f(x) \), which will be upward-curving and in the first quadrant.
- Look for the graph of \( g(x) \), which will be a downward curve that starts at the origin (0,0) and extends downwards, reflecting the stretch factor.
If you can provide descriptions of the images, I can assist you in identifying the correct one.
1. **Base function \( f(x) = \sqrt{x} \)**:
- This graph starts at the origin (0,0) and increases slowly as x increases. It is a curve that lies in the first quadrant.
2. **Stretched function \( g(x) = -\frac{3}{2} \sqrt{x} \)**:
- This function is a vertical stretch of the base function \( f(x) \) by a factor of \(-\frac{3}{2}\), meaning it reflects the graph of \( f(x) \) across the x-axis and stretches it vertically.
- Since it is negative, the graph will be entirely below the x-axis, starting at the origin and moving downwards as x increases.
When comparing the graphs:
- Look for the graph of \( f(x) \), which will be upward-curving and in the first quadrant.
- Look for the graph of \( g(x) \), which will be a downward curve that starts at the origin (0,0) and extends downwards, reflecting the stretch factor.
If you can provide descriptions of the images, I can assist you in identifying the correct one.