Determine When a Function is Even or Odd

The video tutorial explains the concepts of even and odd functions, focusing on their symmetry properties. It provides formal definitions and examples, illustrating how to determine if a function is even, odd, or neither using algebraic methods. The tutorial includes practice problems to reinforce understanding, guiding viewers through the process of identifying function types based on input-output relationships and symmetry.

What is the symmetry property of an even function?

• No symmetry

• Symmetrical with the origin

• Symmetrical with the Y-axis

• Symmetrical with the X-axis

Which of the following is true for an odd function?

• Symmetrical with the Y-axis

• No symmetry

• Symmetrical with the X-axis

• Symmetrical with the origin

If f(-x) = f(x), what type of function is it?

• Neither

• Both

• Even function

• Odd function

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

• It becomes zero

• It becomes undefined

• It remains negative

• It becomes positive

What is the result of raising a negative number to an odd power?

• Positive number

• Undefined

• Negative number

• Zero

How do you determine if a function is odd?

• Check if f(x) is undefined

• Check if f(-x) = f(x)

• Check if f(x) = 0

• Check if f(-x) = -f(x)

Which function is neither even nor odd?

• f(x) = x^2 + x

• f(x) = x^3

• f(x) = x^2

• f(x) = x^4

What is the first step in determining if a function is even or odd?

• Differentiate the function

• Plug in f(-x)

• Integrate the function

• Graph the function

What is the result of f(-x) for an even function?

• 0

• f(x)

• Undefined

• -f(x)

In the practice problems, what indicates a function is odd?

• f(-x) = f(x)

• f(-x) = -f(x)

• f(x) = 0

• f(x) is undefined