Even and Odd Functions

Front

What is an even function?

Back

A function f(x) is called an even function if for every x in the domain, f(-x) = f(x). The graph of an even function is symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is called an odd function if for every x in the domain, f(-x) = -f(x). The graph of an odd function is symmetric about the origin.

Front

What does it mean if a function is neither even nor odd?

Back

A function is neither even nor odd if it does not satisfy the conditions for being even or odd. Its graph does not exhibit symmetry about the y-axis or the origin.

Front

Example of an even function: f(x) = x^2. Is it even, odd, or neither?

Back

Even. Since f(-x) = (-x)^2 = x^2 = f(x).

Front

Example of an odd function: f(x) = x^3. Is it even, odd, or neither?

Back

Odd. Since f(-x) = (-x)^3 = -x^3 = -f(x).

Front

Example of a function that is neither even nor odd: f(x) = x + 1. Is it even, odd, or neither?

Back

Neither. Since f(-x) = -x + 1, which is not equal to f(x) or -f(x).

Front

What is the graphical representation of an even function?

Back

The graph of an even function is symmetric with respect to the y-axis.

Front

What is the graphical representation of an odd function?

Back

The graph of an odd function is symmetric with respect to the origin.

Front

If f(x) = x^4 + x^2, is it even, odd, or neither?

Back

Even. Since f(-x) = (-x)^4 + (-x)^2 = x^4 + x^2 = f(x).

Front

If f(x) = x^3 + 2x, is it even, odd, or neither?

Back

Odd. Since f(-x) = (-x)^3 + 2(-x) = -x^3 - 2x = -f(x).