Exploring Even and Odd Functions

The video tutorial covers the concepts of even and odd functions, explaining their definitions, properties, and how to verify them both algebraically and graphically. It includes examples of even and odd functions, such as quadratic and cubic functions, and demonstrates how to use a calculator to analyze their graphs. The tutorial emphasizes the symmetry properties of these functions, with even functions being symmetric about the y-axis and odd functions being symmetric about the origin.

What is the defining property of an even function?

• f(-x) = -f(x)

• f(x) = f(-x)

• f(-x) = f(x)

• f(x) = -f(x)

Which of the following is an example of an even function?

• y = x^3

• y = x

• y = |x|

• y = 1/x

How can you determine if a function is even algebraically?

• Check if f(x) = -f(x)

• Check if f(-x) = -f(x)

• Check if f(x) = f(-x)

• Check if f(-x) = f(x)

What is the defining property of an odd function?

• f(-x) = f(x)

• f(-x) = -f(x)

• f(x) = -f(x)

• f(x) = f(-x)

Which of the following is an example of an odd function?

• y = |x|

• y = x^2

• y = x^4

• y = x^3

How can you determine if a function is odd algebraically?

• Check if f(x) = f(-x)

• Check if f(x) = -f(x)

• Check if f(-x) = -f(x)

• Check if f(-x) = f(x)

If h(3) = -5, what is h(-3) for an even function?

• Cannot be determined

• 0

• 5

• -5

Which of the following graphs represents an even function?

• A graph symmetric about the y-axis

• A graph with no symmetry

• A graph symmetric about the x-axis

• A graph symmetric about the origin

If h(3) = -5, what is h(-3) for an odd function?

• -5

• 5

• Cannot be determined

• 0

Which of the following graphs represents an odd function?

• A graph symmetric about the y-axis

• A graph symmetric about the x-axis

• A graph symmetric about the origin

• A graph with no symmetry