Determine visually whether the graph is symmetric with respect to the -axis, the -axis, or the
origin.
Choose the correct answer below.
A. -axis
B. -axis
C. origin
D. both -axis and -axis

Ask by Schneider Pierce. in the United States

Jan 25,2025

Question

Determine visually whether the graph is symmetric with respect to the -axis, the -axis, or the
origin.
Choose the correct answer below.
A. -axis
B. -axis
C. origin
D. both -axis and -axis

Ask by Schneider Pierce. in the United States

Jan 25,2025

UpStudy AI · Accepted Answer

I'm unable to view the graph you're referring to, but I can help you determine symmetry based on the general principles. Here's how you can check for different types of symmetry in a graph:

1. **Symmetry with respect to the $$ y $$-axis**:
   - **Test**: Replace $$ x $$ with $$ -x $$ in the equation of the graph.
   - **If the equation remains unchanged**, the graph is symmetric about the $$ y $$-axis.
   - **Example**: The equation $$ y = x^2 $$ is symmetric about the $$ y $$-axis.

2. **Symmetry with respect to the $$ x $$-axis**:
   - **Test**: Replace $$ y $$ with $$ -y $$ in the equation of the graph.
   - **If the equation remains unchanged**, the graph is symmetric about the $$ x $$-axis.
   - **Note**: Most functions do not have $$ x $$-axis symmetry because this would imply they are not functions (they would fail the vertical line test).

3. **Symmetry with respect to the origin**:
   - **Test**: Replace both $$ x $$ with $$ -x $$ and $$ y $$ with $$ -y $$ in the equation of the graph.
   - **If the equation remains unchanged**, the graph is symmetric about the origin.
   - **Example**: The equation $$ y = x^3 $$ is symmetric about the origin.

4. **Symmetry with respect to both the $$ x $$-axis and the $$ y $$-axis**:
   - **Condition**: The graph must satisfy both the $$ x $$-axis and $$ y $$-axis symmetry conditions individually.
   - **Example**: The equation $$ y^2 = x^2 $$ (which represents two lines, $$ y = x $$ and $$ y = -x $$) is symmetric about both axes.

**How to Choose the Correct Answer:**

- **A. $$ x $$-axis**: If only the $$ x $$-axis symmetry condition is satisfied.
- **B. $$ y $$-axis**: If only the $$ y $$-axis symmetry condition is satisfied.
- **C. Origin**: If only the origin symmetry condition is satisfied.
- **D. Both $$ x $$-axis and $$ y $$-axis**: If both the $$ x $$-axis and $$ y $$-axis symmetries are satisfied.

**Example Application:**

Suppose you're given the graph of $$ y = x^2 $$.

- Replace $$ x $$ with $$ -x $$: $$ y = (-x)^2 = x^2 $$ (unchanged) → Symmetric about the $$ y $$-axis.
- Replace $$ y $$ with $$ -y $$: $$ -y = x^2 $$ → Not the same as the original equation → Not symmetric about the $$ x $$-axis.
- Replace both $$ x $$ with $$ -x $$ and $$ y $$ with $$ -y $$: $$ -y = (-x)^2 = x^2 $$ → Not the same as the original equation → Not symmetric about the origin.

**Conclusion for the Example:** The graph is symmetric with respect to the $$ y $$-axis. Therefore, the correct answer would be **B. $$ y $$-axis**.

If you can provide more details about the graph or its equation, I'd be happy to help you determine its symmetry more specifically!
To determine the symmetry of the graph, check each axis: - **$$ y $$-axis**: Replace $$ x $$ with $$ -x $$. If the equation remains the same, it's symmetric about the $$ y $$-axis. - **$$ x $$-axis**: Replace $$ y $$ with $$ -y $$. If the equation remains the same, it's symmetric about the $$ x $$-axis. - **Origin**: Replace both $$ x $$ with $$ -x $$ and $$ y $$ with $$ -y $$. If the equation remains the same, it's symmetric about the origin. Choose the correct option based on which symmetry condition is satisfied. **Answer:** - **A. $$ x $$-axis** - **B. $$ y $$-axis** - **C. Origin** - **D. Both $$ x $$-axis and $$ y $$-axis** If the graph is symmetric about the $$ y $$-axis, select **B. $$ y $$-axis**.

Determine visually whether the graph is symmetric with respect to the -axis, the -axis, or the
origin.
Choose the correct answer below.
A. -axis
B. -axis
C. origin
D. both -axis and -axis

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Determine visually whether the graph is symmetric with respect to the -axis, the -axis, or the origin. Choose the correct answer below. A. -axis B. -axis C. origin D. both -axis and -axis

Solución de inteligencia artificial de Upstudy

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Solución

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preguntas relacionadas

Latest Geometry Questions

Determine visually whether the graph is symmetric with respect to the -axis, the -axis, or the
origin.
Choose the correct answer below.
A. -axis
B. -axis
C. origin
D. both -axis and -axis