Even Odd Function Graph

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

How can you determine if a function is even, odd, or neither from its graph?

Back

To determine if a function is even, check for y-axis symmetry. For odd functions, check for origin symmetry. If neither symmetry is present, the function is neither even nor odd.

Front

What is the significance of symmetry in even and odd functions?

Back

Symmetry helps in understanding the behavior of functions, simplifying calculations, and predicting the function's values at certain points.

Front

Can a function be both even and odd?

Back

Yes, the only function that is both even and odd is the zero function, f(x) = 0, since it satisfies both conditions.

Front

What is an example of an even function?

Back

An example of an even function is f(x) = x^2, as it satisfies the condition f(-x) = f(x).

Front

What is an example of an odd function?

Back

An example of an odd function is f(x) = x^3, as it satisfies the condition 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

How do you test if a function is even or odd using algebra?

Back

To test if a function is even, substitute -x into the function and see if it equals the original function. To test if it is odd, substitute -x and see if it equals the negative of the original function.