Determining Even, Odd, or Neither Functions

The video tutorial explains how to determine if a function is even, odd, or neither by substituting negative x for x and simplifying. It covers three examples: the first function is identified as odd, the second as even, and the third as neither. The process involves checking if the simplified function equals the original or its negative. The video concludes with a call to action to like and subscribe.

What is the first step in determining if a function is even, odd, or neither?

• Substitute negative x for x

• Compare with the original function

• Simplify the function

• Factor out a negative sign

What do you get when you substitute negative x into the function x^5 + x?

• x^5 - x

• x^5 + x

• Negative x^5 - x

• Negative x^5 + x

How do you determine that the function x^5 + x is odd?

• It simplifies to the original function

• It simplifies to the negative of the original function

• It simplifies to zero

• It does not simplify

What is the result of substituting negative x into the function 1 - x^4?

• 1 + x^4

• 1 - x^4

• Negative 1 - x^4

• Negative 1 + x^4

What conclusion can be drawn if a function simplifies back to its original form after substituting negative x?

• The function is undefined

• The function is neither

• The function is even

• The function is odd

What is the result of substituting negative x into the function 2x - x^2?

• 2x - x^2

• Negative 2x + x^2

• 2x + x^2

• Negative 2x - x^2

Why is the function 2x - x^2 neither even nor odd?

• It does not simplify to either the original or its negative

• It simplifies to the negative of the original function

• It simplifies to the original function

• It simplifies to zero

What is the key indicator that a function is odd?

• It simplifies to the original function

• It simplifies to the negative of the original function

• It simplifies to zero

• It does not simplify

What is the key indicator that a function is even?

• It simplifies to the original function

• It simplifies to the negative of the original function

• It does not simplify

• It simplifies to zero

What should you do if a function does not simplify to either the original or its negative?

• Call it even

• Call it odd

• Call it neither

• Call it undefined