Even and Odd Functions

This video tutorial from Howard Community College explains how to determine if a function is even, odd, or neither. It covers the symmetry properties of even and odd functions, provides examples, and demonstrates tests to identify function types. The video concludes with a summary of the steps to determine function types.

What is the main topic discussed in this video?

• Calculating derivatives

• Graphing linear functions

• Determining if a function is even, odd, or neither

• How to solve quadratic equations

What characteristic defines an even function?

• Symmetry with respect to the origin

• Symmetry with respect to the x-axis

• Symmetry with respect to the y-axis

• No symmetry

How can you test if a function is even?

• Check if f(x) = x

• Check if f(x) = 0

• Check if f(x) = f(-x)

• Check if f(x) = -f(x)

What is the symmetry of an even function?

• Symmetry with respect to the x-axis

• Symmetry with respect to the y-axis

• Symmetry with respect to the origin

• No symmetry

What is the test for an even function?

• f(x) = -f(x)

• f(x) = x

• f(-x) = f(x)

• f(x) = 0

In the example f(x) = 3x^4 - 5x^2 + 12, what is f(-x)?

• 3x^4 + 5x^2 + 12

• 3x^4 - 5x^2 - 12

• 3x^4 - 5x^2 + 12

• -3x^4 - 5x^2 + 12

What conclusion is drawn about the function f(x) = 3x^4 - 5x^2 + 12?

• It is an even function

• It is neither even nor odd

• It is a linear function

• It is an odd function

What happens to a negative number raised to an even power?

• It becomes zero

• It remains the same

• It becomes positive

• It becomes negative

What is the result of f(-x) for the function f(x) = 3x^4 - 5x^2 + 12?

• -3x^4 + 5x^2 - 12

• 3x^4 - 5x^2 + 12

• 3x^4 + 5x^2 + 12

• -3x^4 - 5x^2 + 12

What is the result of -f(x) for the function f(x) = 3x^4 - 5x^2 + 12?

• -3x^4 + 5x^2 - 12

• -3x^4 - 5x^2 + 12

• 3x^4 + 5x^2 + 12

• 3x^4 - 5x^2 - 12