Understanding Even and Odd Functions

The video tutorial explores the concepts of even and odd functions. It begins with definitions, explaining that even functions satisfy f(-x) = f(x) and odd functions satisfy f(-x) = -f(x). The tutorial then analyzes three functions: h(x), f(x), and g(x). Through detailed calculations, it demonstrates that h(x) is odd, f(x) is even, and g(x) is neither. The video emphasizes the importance of recognizing patterns in exponents to determine function parity.

What is the defining property of an even function?

• f(-x) = -f(x)

• f(x) = 0

• f(-x) = f(x)

• f(x) = x

What happens to the signs of the terms in h(x) when you evaluate h(-x)?

• All signs change

• Only odd-powered terms change signs

• Only even-powered terms change signs

• All signs remain the same

Why is h(x) classified as an odd function?

• It is symmetric about the x-axis

• It has only odd exponents

• It has only even exponents

• It is symmetric about the y-axis

Which function is made up of terms with only odd degrees?

• None of the above

• f(x)

• g(x)

• h(x)

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

• f(-x) = -f(x)

• f(-x) = f(x)

• f(-x) = 0

• f(-x) = 2f(x)

What characteristic of f(x) makes it an even function?

• It is symmetric about the x-axis

• It is neither even nor odd

• It has only even exponents

• It has only odd exponents

Which function is made up of terms with only even degrees?

• None of the above

• g(x)

• f(x)

• h(x)

What is the nature of g(x) based on its terms?

• Even

• Odd

• Neither even nor odd

• Both even and odd

Why is g(x) neither even nor odd?

• It is symmetric about the y-axis

• It has only odd terms

• It has only even terms

• It has both even and odd terms

What happens to the signs of the odd-powered terms in g(x) when evaluating g(-x)?

• They double

• They change

• They remain the same

• They become zero