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  1. Compare whether each function below is an even function, an odd function, or neither. Homework Help ✎

    1. f(x) = x2

    2. f(x) = x3

    3. f(x) = 2x

    4. f(x) = sin x

Definition of an even function: f(a) = f(−a)
Definition of an odd function: f(−a) = −f(a)

f(x) = x²
f(a) = (a)²= a²
f(−a) = (−a)²= a².......... f(a) = f(−a) it's even!
f(a) = −(a)²= −a².............f(−a) ≠ −f(a) it's NOT odd.

Refer to hint and steps in part (a).

Refer to hint and steps in part (a).

Even functions are symmetrical over the y-axis.
Odd functions are symmetrical about the origin.

Sketch a graph of sinx and describe the symmetry.