Exploring Adding and Subtracting Rational Expressions

In this video, Gabe explains how to determine if a polynomial function is odd, even, or neither. He reviews the definitions of odd and even functions, then analyzes the given polynomial function by substituting negative x for x. Through step-by-step calculations, he shows that f(-x) equals f(x), concluding that the function is even.

What is the polynomial function given in the problem?

• f(x) = x^4 + 2x^2 - 3

• f(x) = x^2 + 3x^2 - 2

• f(x) = x^4 + 3x^2 - 2

• f(x) = x^3 + 3x - 2

What does it mean for a function to be odd?

• f(x) = -f(-x)

• f(-x) = -f(x)

• f(-x) = f(x)

• f(x) = f(-x)

What does it mean for a function to be even?

• f(-x) = -f(x)

• f(x) = f(-x)

• f(-x) = f(x)

• f(x) = -f(-x)

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

• Integrate the function

• Simplify the function

• Substitute -x into the function

• Differentiate the function

What is the result of raising -x to the 4th power?

• x^2

• -x^2

• x^4

• -x^4

What is the result of squaring -x?

• -x^2

• x^2

• -x

• x

What is the simplified form of f(-x) for the given function?

• x^4 - 3x^2 - 2

• x^4 + 3x^2 + 2

• x^4 + 3x^2 - 2

• x^4 - 3x^2 + 2

What do we conclude if f(-x) equals f(x)?

• The function is both odd and even

• The function is neither odd nor even

• The function is even

• The function is odd

What is the final conclusion about the given function?

• The function is both odd and even

• The function is odd

• The function is even

• The function is neither odd nor even