How to determine if a function is even odd or neither

The video tutorial explains how to determine if a function is even, odd, or neither by analyzing its symmetry graphically and algebraically. Even functions are symmetrical about the Y-axis, while odd functions are symmetrical about the origin. The tutorial provides methods to test functions algebraically by substituting negative values and checking for symmetry. It emphasizes understanding the concepts through graphical examples and algebraic testing, ensuring clarity in identifying function types.

What is a key characteristic of an even function when viewed graphically?

• Symmetrical about the X-axis

• Symmetrical about the Y-axis

• Symmetrical about the origin

• No symmetry

How can you identify an odd function graphically?

• It has no symmetry

• It is symmetrical about the X-axis

• It is symmetrical about the origin

• It is symmetrical about the Y-axis

What is the first step in the algebraic method to determine if a function is even?

• Reflect the function over the X-axis

• Evaluate the function at X = 0

• Substitute negative X into the function

• Check if the function is symmetrical about the origin

If a function is even, what should be true when you substitute -X into the function?

• The output should be the same as F(X)

• The output should be the opposite of F(X)

• The output should be zero

• The output should be undefined

What is the algebraic test for determining if a function is odd?

• Substitute X and check if the output is zero

• Substitute X and check if the output is undefined

• Substitute -X and check if the output is the opposite of F(X)

• Substitute -X and check if the output is the same as F(X)

What does it mean if substituting -X into a function results in neither the same nor the opposite of F(X)?

• The function is odd

• The function is even

• The function is undefined

• The function is neither even nor odd

Which of the following is true for a function that is neither even nor odd?

• It has no symmetry

• It is symmetrical about the origin

• It is symmetrical about the X-axis

• It is symmetrical about the Y-axis