Even and Odd Functions

Front

What is an even function?

Back

A function f(x) is called an even function if f(-x) = f(x) for all x in the domain of f. Graphically, even functions are symmetric about the y-axis.

Front

What is an odd function?

Back

A function f(x) is called an odd function if f(-x) = -f(x) for all x in the domain of f. Graphically, odd functions are 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. This means that f(-x) is not equal to f(x) or -f(x) for all x.

Front

Back

Neither even nor odd.

Front

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

Back

The function is an even function.

Front

Back

Odd function.

Front

What is the graphical representation of an even function?

Back

Even functions are symmetric with respect to the y-axis.

Front

What is the graphical representation of an odd function?

Back

Odd functions are symmetric with respect to the origin.

Front

If a function is represented by a graph that is symmetric about the y-axis, what type of function is it?

Back

It is an even function.

Front

If a function is represented by a graph that is symmetric about the origin, what type of function is it?

Back

It is an odd function.