Problem 102
Question
If you are given a function's equation, how do you determine if the function is even, odd, or neither?
Step-by-Step Solution
Verified Answer
To determine if a function is even, odd, or neither, substitute \(-x\) into the function for \(x\). If the function is unchanged, it is even. If the negated function matches the original, it is odd. If neither of these match, the function is neither even nor odd.
1Step 1: Try to See if the Function is Even
Substitute \(-x\) into the equation for \(x\). Simplify the function accordingly. If the resulting function matches the original function, the function is even.
2Step 2: Try to See if the Function is Odd
If the function isn't even, substitute \(-x\) into the equation for \(x\). Then multiply the function by -1. If the resulting function matches the original function, the function is odd.
3Step 3: Function is Neither
If the function does not match the original equation after either of these substitutions and simplifications, the function is neither even nor odd.
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