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 function is even from its graph?

Back

A function is even if the left side of the graph is a mirror image of the right side when folded along the y-axis.

Front

How can you determine if a function is odd from its graph?

Back

A function is odd if rotating the graph 180 degrees around the origin results in the same graph.

Front

Give an example of an even function.

Back

f(x) = x^2 is an even function because f(-x) = (-x)^2 = x^2.

Front

Give an example of an odd function.

Back

f(x) = x^3 is an odd function because f(-x) = (-x)^3 = -x^3.

Front

What is the significance of the y-axis in even functions?

Back

The y-axis acts as a line of symmetry for even functions, meaning the function's values are the same for x and -x.

Front

What is the significance of the origin in odd functions?

Back

The origin acts as a point of symmetry for odd functions, meaning if you rotate the graph 180 degrees around the origin, it remains unchanged.

Front

Can a function be both even and odd?

Back

Yes, the only function that is both even and odd is the constant function f(x) = 0.