Learn to Show That a Function is Odd Algebraically

The video tutorial explains how to determine if a function is odd. It begins by discussing the properties of negative numbers raised to odd powers and introduces the concept of odd functions. The tutorial then outlines the test for odd functions, which involves checking if the function equals the negative of itself. Finally, it concludes by confirming the function type as odd.

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

• It becomes zero.

• It remains negative.

• It becomes even.

• It becomes positive.

Which of the following is a test to determine if a function is odd?

• If f(x) equals 0

• If f(-x) equals -f(x)

• If f(x) equals -f(x)

• If f(x) equals f(-x)

What must be true for a function to be classified as odd?

• f(x) = 0

• f(-x) = f(x)

• f(x) = -f(x)

• f(x) = f(-x)

What type of function is confirmed in the final section?

• Even

• Odd

• Quadratic

• Linear

What is the significance of comparing f(x) to -f(x)?

• To determine if the function is odd

• To determine if the function is linear

• To determine if the function is even

• To determine if the function is quadratic