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. Its graph does not exhibit symmetry with respect to the y-axis or the origin.

Front

Back

Even Function (since f(-x) = (-x)^2 = x^2 = f(x)).

Front

Back

Odd Function (since f(-x) = (-x)^3 = -x^3 = -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) = f(x), what can we conclude about the function?

Back

The function is an even function.

Front

If f(-x) = -f(x), what can we conclude about the function?

Back

The function is an odd function.

Front

Back

Even Function (since all powers of x are even).