Learn to Show When a Function is Odd Algebraically

The video tutorial discusses the properties of negative numbers raised to odd powers, emphasizing that they result in negative values. It explores the concept of function symmetry, determining whether a function is odd or even by testing its behavior. The tutorial concludes with a graphical representation, showing how flipping a graph over the X and Y axes can demonstrate symmetry, particularly for even functions.

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

• Positive

• Negative

• Zero

• Undefined

How can you determine if a function is odd?

• By checking if the function is symmetrical about the Y axis

• By comparing the function to its opposite

• By ensuring the function is always positive

• By checking if the function is symmetrical about the X axis

What is the opposite of a function f(x)?

• -f(x)

• f(x) + 1

• f(x) * 2

• f(x) - 1

What happens to the graph of an odd function when flipped over the X and Y axes?

• It disappears

• It becomes symmetrical about the Y axis

• It becomes a straight line

• It remains unchanged

Which of the following is true about even functions?

• They are symmetrical about the X axis

• They are symmetrical about the Y axis

• They are always positive

• They are always negative