Exploring Even and Odd Functions

The video tutorial explains how to graph functions by using tables and recognizing symmetry properties. It covers even functions, which are symmetric about the y-axis, and odd functions, which are symmetric around the origin. The tutorial also discusses symmetry in non-function graphs, such as circles, which can have multiple symmetry properties. Understanding these concepts helps in graphing functions more efficiently.

What is one method to graph a function that will always give at least a rough sketch?

• Using a computer program

• Drawing freehand

• Making a table of values

• Using a calculator

What can save you a lot of work when graphing a function?

• Knowing the function's symmetry properties

• Using colored pencils

• Drawing slowly

• Using a ruler

What is an even function?

• A function that is symmetric with respect to the x-axis

• A function that is symmetric with respect to the y-axis

• A function that is not symmetric

• A function that is symmetric with respect to the origin

Why are even functions called 'even'?

• Because they are symmetric with respect to the origin

• Because they have even coefficients

• Because they have even exponents

• Because they are symmetric with respect to the x-axis

How can you determine if a function is even by looking at its equation?

• Check if f(x) = -f(x)

• Check if f(x) = f(-x)

• Check if f(x) = 0

• Check if f(x) = x

What does the graph of an even function look like?

• It is symmetric with respect to the y-axis

• It is not symmetric

• It is symmetric with respect to the x-axis

• It is symmetric with respect to the origin

What is an odd function?

• A function that is symmetric with respect to the origin

• A function that is symmetric with respect to the x-axis

• A function that is symmetric with respect to the y-axis

• A function that is not symmetric

How can you determine if a function is odd by looking at its equation?

• Check if f(x) = f(-x)

• Check if f(x) = -f(x)

• Check if f(x) = -f(-x)

• Check if f(x) = x

What does the graph of an odd function look like?

• It is not symmetric

• It is symmetric with respect to the x-axis

• It is symmetric with respect to the origin

• It is symmetric with respect to the y-axis

Which of the following is an example of a graph that has both even and odd symmetry properties?

• A line

• A parabola

• A cubic function

• A circle