Question
How is the function shown below related to yequalsx? Graph the function by translating the parent function.
yequalsxplus7
Question content area bottom
Part 1
How are the functions related?
A.
Each output of yequalsxplus7 is seven more than the corresponding output for yequalsx.
B.
Each output of yequalsxplus7 is seven times the corresponding output for yequalsx.
C.
Each output of yequalsxplus7 is one-seventh the corresponding output for yequalsx.
D.
Each output of yequalsxplus7 is seven less than the corresponding output for yequalsx.
yequalsxplus7
Question content area bottom
Part 1
How are the functions related?
A.
Each output of yequalsxplus7 is seven more than the corresponding output for yequalsx.
B.
Each output of yequalsxplus7 is seven times the corresponding output for yequalsx.
C.
Each output of yequalsxplus7 is one-seventh the corresponding output for yequalsx.
D.
Each output of yequalsxplus7 is seven less than the corresponding output for yequalsx.
Answers
Answered by
GPT-4o mini
To understand how the function \( y = x + 7 \) is related to the parent function \( y = x \), we can analyze the transformation that occurs.
The function \( y = x + 7 \) represents a vertical translation of the parent function \( y = x \). Specifically, it can be understood as shifting the entire graph of \( y = x \) upward by 7 units.
Now let's evaluate the provided options:
A. **Each output of \( y = x + 7 \) is seven more than the corresponding output for \( y = x \).**
- This is correct because for any input \( x \), the output of \( y = x + 7 \) is simply the output of \( y = x \) plus 7.
B. **Each output of \( y = x + 7 \) is seven times the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not multiplied; they are increased by 7.
C. **Each output of \( y = x + 7 \) is one-seventh the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not scaled down; they are not in any way related to being a fraction of the outputs of the parent function.
D. **Each output of \( y = x + 7 \) is seven less than the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not decreased; they are increased by 7, not decreased.
Thus, the correct relationship is represented by:
**A. Each output of \( y = x + 7 \) is seven more than the corresponding output for \( y = x.**
The function \( y = x + 7 \) represents a vertical translation of the parent function \( y = x \). Specifically, it can be understood as shifting the entire graph of \( y = x \) upward by 7 units.
Now let's evaluate the provided options:
A. **Each output of \( y = x + 7 \) is seven more than the corresponding output for \( y = x \).**
- This is correct because for any input \( x \), the output of \( y = x + 7 \) is simply the output of \( y = x \) plus 7.
B. **Each output of \( y = x + 7 \) is seven times the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not multiplied; they are increased by 7.
C. **Each output of \( y = x + 7 \) is one-seventh the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not scaled down; they are not in any way related to being a fraction of the outputs of the parent function.
D. **Each output of \( y = x + 7 \) is seven less than the corresponding output for \( y = x \).**
- This is incorrect. The outputs are not decreased; they are increased by 7, not decreased.
Thus, the correct relationship is represented by:
**A. Each output of \( y = x + 7 \) is seven more than the corresponding output for \( y = x.**