Odd Function: If replacing \(x\) with \(−x\) gives the negative of the function, it’s symmetric about the origin.Even Function: If replacing \(x\) with \(−x\) yields the same function, it’s symmetric about the \(y\)-axis.The resulting value is where the graph crosses the \(y\)-axis. \(Y\)-intercept: Plug in \(x=0\) into your polynomial.\(X\)-intercepts: Points where the graph crosses or touches the \(x\)-axis (same as zeros).These can be found using calculus or by analyzing the nature of zeros and their multiplicities. Maximum & Minimum: Understand that the graph can have high and low points between zeros.Even degree: Ends move in the same direction.Degree & Leading Coefficient: These determine how the graph behaves as \(x\) approaches positive or negative infinity.Factorization: Use techniques like factoring, the quadratic formula, or synthetic division to find zeros.They play a pivotal role in shaping the graph. Locate Zeros: These are the \(x\)-values where the function touches or crosses the \(x\)-axis.Higher Degrees: Understand the potential wiggles and turns the graph might have e.g., a cubic can have a single curve or an S-shape.
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