Even and Odd Functions Flashcard

Front

What is an even function?

Back

A function f(x) is called even if for every x in the domain, f(-x) = f(x).

Front

What is an odd function?

Back

A function f(x) is called odd if for every x in the domain, f(-x) = -f(x).

Front

Identify an example of an even function.

Back

f(x) = x^2 + 1 is an example of an even function.

Front

Identify an example of an odd function.

Back

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

Front

What is the graphical representation of an even function?

Back

Even functions are symmetric about the y-axis.

Front

What is the graphical representation of an odd function?

Back

Odd functions are symmetric about the origin.

Front

If f(x) = x^2, what is f(-x)?

Back

f(-x) = (-x)^2 = x^2, confirming f(x) is even.

Front

If f(x) = x^3, what is f(-x)?

Back

f(-x) = (-x)^3 = -x^3, confirming f(x) is odd.

Front

What is the property of even functions regarding their derivatives?

Back

The derivative of an even function is an odd function.

Front

What is the property of odd functions regarding their derivatives?

Back

The derivative of an odd function is an even function.