How do you test a graph equation for x-axis symmetry?
To test a graph equation for x-axis symmetry, you can follow these steps:
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To test a graph equation for x-axis symmetry, you can follow these steps:
1. Rewrite the equation in the form f(x) = y. This means you need to isolate the y term on one side of the equation.
2. Replace y with -y in the equation. This reflects the graph across the x-axis.
3. Simplify the equation and see if it remains the same. If the equation remains unchanged, then the graph is symmetric with respect to the x-axis.
For example, let’s say we have the equation y = x^2. To test for x-axis symmetry:
1. Rewrite the equation as f(x) = x^2.
2. Replace y with -y: f(x) = -x^2.
3. Simplify the equation: -f(x) = x^2.
The equation has changed, indicating that the graph is not symmetric with respect to the x-axis.
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