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). This means the graph of the function is symmetric with respect to 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). This means the graph of the function is symmetric with respect to 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. This means that f(-x) is not equal to f(x) or -f(x) for all x in the domain.

Front

Back

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

Front

Back

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

Front

Identify the even function from the following: f(x) = x^4 + 2, g(x) = x^3 + 1, h(x) = x^2 - 5.

Back

f(x) = x^4 + 2. It satisfies f(-x) = f(x).

Front

Identify the odd function from the following: f(x) = x^2 + 1, g(x) = 2x^3 - 3x, h(x) = x^4 - 4.

Back

g(x) = 2x^3 - 3x. It satisfies f(-x) = -f(x).

Front

What is the graphical representation of an even function?

Back

The graph of an even function is symmetric about the y-axis.

Front

What is the graphical representation of an odd function?

Back

The graph of an odd function is symmetric about the origin.

Front

If f(x) = 2x^2 + 4, what can be said about its symmetry?

Back

The function is even because f(-x) = f(x).