Problem

Given the function f(x)=−2x3+3x2−2x+1, determine whether it is symmetrical about the y-axis (even), symmetrical about the origin (odd), or neither.

Answer

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Answer

Next, we check if the function is odd. A function is odd if it satisfies the condition f(−x)=−f(x). We compare f(−x) and −f(x): −f(x)=2x3−3x2+2x−1. This is also not equal to f(−x), so the function is not odd.

Steps

Step 1 ：First, we check if the function is even. A function is even if it satisfies the condition f(−x)=f(x). We compute f(−x): −2(−x)3+3(−x)2−2(−x)+1=−2x3+3x2+2x+1. This is not equal to f(x), so the function is not even.

Step 2 ：Next, we check if the function is odd. A function is odd if it satisfies the condition f(−x)=−f(x). We compare f(−x) and −f(x): −f(x)=2x3−3x2+2x−1. This is also not equal to f(−x), so the function is not odd.

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