Question 9 of 10
How would you describe the difference between the graphs of
and ?
A. is a reflection of over the -axis.
B. is a reflection of over the line
D. is a reflection of over the line .
Deflection of over the -axis.

Ask by Craig Fleming. in the United States

Nov 07,2024

Question

Question 9 of 10
How would you describe the difference between the graphs of
and ?
A. is a reflection of over the -axis.
B. is a reflection of over the line
D. is a reflection of over the line .
Deflection of over the -axis.

Ask by Craig Fleming. in the United States

Nov 07,2024

UpStudy AI · Accepted Answer

To analyze the functions $$ f(x) = x^2 + 4 $$ and $$ g(y) = y^2 + 4 $$, we need to understand their graphs and how they relate to each other.

1. **Graph of $$ f(x) = x^2 + 4 $$**:
   - This is a parabola that opens upwards with its vertex at the point $$ (0, 4) $$. The graph is symmetric about the $$ y $$-axis.

2. **Graph of $$ g(y) = y^2 + 4 $$**:
   - This is also a parabola that opens upwards, but it is expressed in terms of $$ y $$. If we rewrite it in terms of $$ x $$, we can express it as $$ x = y^2 + 4 $$. This means that for each value of $$ y $$, there is a corresponding value of $$ x $$.

Now, let's analyze the options:

A. **$$ g(y) $$ is a reflection of $$ f(x) $$ over the $$ y $$-axis.**
   - This is incorrect. The graphs are not reflections over the $$ y $$-axis; they are different representations of parabolas.

B. **$$ g(y) $$ is a reflection of $$ f(x) $$ over the line $$ y=1 $$.**
   - This is also incorrect. The graphs do not reflect over the line $$ y=1 $$.

C. **$$ g(y) $$ is a reflection of $$ f(x) $$ over the line $$ y=x $$.**
   - This is correct. The graph of $$ g(y) $$ can be obtained by reflecting the graph of $$ f(x) $$ over the line $$ y=x $$.

D. **Deflection of $$ f(x) $$ over the $$ x $$-axis.**
   - This is incorrect. The graphs do not reflect over the $$ x $$-axis.

Thus, the correct answer is:

**C. $$ g(y) $$ is a reflection of $$ f(x) $$ over the line $$ y=x $$.**
The correct answer is C. $$ g(y) $$ is a reflection of $$ f(x) $$ over the line $$ y=x $$.

Question 9 of 10
How would you describe the difference between the graphs of
and ?
A. is a reflection of over the -axis.
B. is a reflection of over the line
D. is a reflection of over the line .
Deflection of over the -axis.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Question 9 of 10 How would you describe the difference between the graphs of and ? A. is a reflection of over the -axis. B. is a reflection of over the line D. is a reflection of over the line . Deflection of over the -axis.

Upstudy AI Solution

Answer

Solution

Mind Expander

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Latest Pre Calculus Questions

Question 9 of 10
How would you describe the difference between the graphs of
and ?
A. is a reflection of over the -axis.
B. is a reflection of over the line
D. is a reflection of over the line .
Deflection of over the -axis.