Determine if the given relation $$ x=1 \cdot y^{2}+4 $$ is symmetrical to the $$ x $$-axis, $$ y $$-axis, the origin, or none. origin symmetry $$ x $$-axis symmetry $$ y $$-axis symmetry none

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To determine the symmetry of the relation $$ x = y^{2} + 4 $$, let's analyze it with respect to the three types of symmetries: $$ y $$-axis, $$ x $$-axis, and the origin.

1. **$$ y $$-Axis Symmetry:**
   - **Test:** Replace $$ x $$ with $$ -x $$ in the equation.
   - **Result:** $$ -x = y^{2} + 4 $$
   - **Conclusion:** This is not equivalent to the original equation $$ x = y^{2} + 4 $$. Therefore, the relation **does not** have $$ y $$-axis symmetry.

2. **$$ x $$-Axis Symmetry:**
   - **Test:** Replace $$ y $$ with $$ -y $$ in the equation.
   - **Result:** $$ x = (-y)^{2} + 4 $$ simplifies to $$ x = y^{2} + 4 $$
   - **Conclusion:** This is identical to the original equation. Therefore, the relation **does** have $$ x $$-axis symmetry.

3. **Origin Symmetry:**
   - **Test:** Replace $$ x $$ with $$ -x $$ and $$ y $$ with $$ -y $$ in the equation.
   - **Result:** $$ -x = (-y)^{2} + 4 $$ simplifies to $$ -x = y^{2} + 4 $$
   - **Conclusion:** This is not equivalent to the original equation $$ x = y^{2} + 4 $$. Therefore, the relation **does not** have origin symmetry.

**Final Answer:**  
The relation is symmetric about the $$ x $$-axis.
The relation is symmetric about the $$ x $$-axis.

Determine if the given relation is symmetrical to the -axis, -axis, the origin, or none.
origin symmetry
-axis symmetry
-axis symmetry
none

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Determine if the given relation is symmetrical to the -axis, -axis, the origin, or none. origin symmetry -axis symmetry -axis symmetry none