Problem 118
Question
Given an equation in \(x\) and \(y,\) how do you determine if its graph is symmetric with respect to the \(y\) -axis?
Step-by-Step Solution
Verified Answer
To determine if an equation is symmetric with respect to the y-axis, replace every x in the equation with -x and simplify the equation. If the new equation is identical to the original, then the graph is symmetric with respect to the y-axis.
1Step 1: Substitute x with -x
Replace every x in the equation with -x.
2Step 2: Simplification
Simplify the equation after substituting x with -x. Try to get an equation that looks identical to the original equation. If it's the same, then the equation is symmetric with respect to the y-axis.
3Step 3: Verification
Compare the simplified equation obtained in step 2 with the original equation. If they're the same, the graph is symmetric with respect to the y-axis.
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