even and odd functions from 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 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 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

How can you determine if a graph is even?

Back

To determine if a graph is even, check if the graph is symmetric about the y-axis. If f(-x) = f(x) for all x, then the function is even.

Front

How can you determine if a graph is odd?

Back

To determine if a graph is odd, check if the graph is symmetric about the origin. If f(-x) = -f(x) for all x, then the function is odd.

Front

Give an example of an even function.

Back

An example of an even function is f(x) = x^2. For this function, f(-x) = (-x)^2 = x^2 = f(x).

Front

Give an example of an odd function.

Back

An example of an odd function is f(x) = x^3. For this function, f(-x) = (-x)^3 = -x^3 = -f(x).

Front

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

Back

Symmetry helps in graphing functions and understanding their behavior. Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.

Front

Can a function be both even and odd?

Back

Yes, a function can be both even and odd if it is the zero function, f(x) = 0, since f(-x) = 0 = f(x) and f(-x) = -f(x).

Front

What is the graphical representation of an even function?

Back

The graphical representation of an even function shows that for every point (x, f(x)), there is a corresponding point (-x, f(x)).