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## Classifying Even and Odd Functions

#### HS Interpreting Functions - HSF-IF.C.8

How Do You Classify Even and Odd Functions? Just like the concept of even and odd numbers, functions have an even or odd nature to them as well. By graphical definition, a function is even if the graph is symmetric with respect to the y-axis, while, algebraically, a function is even if f(-x)=f(x) for all the x present in the domain. While a function is odd if the function's graph is symmetric to the origin. While algebraically, the function is only odd if f(-x)=-f(x) for all the x present in the domain. Let us consider a function with two values of x and see f(x) =x3 + 4x + 2 , if x = -x, then the equation will become f(-x) = (-x)3 + 4(-x) + 2, f(-x) = (-x)3 - 4x + 2 The value of the function changed, which means that this is an odd function. f(x) = x2+2, if x = - x, then the equation will become f(-x) = (-x)2 + 2, f(-x) = x2 + 2, f(-x) = f(x). The value of the function does not change, which means that this is an even function. Students can use these worksheets and lesson to learn how to identify a function as even or odd.

### Printable Worksheets And Lessons  #### Homework Sheets

Classify the functions as even, odd, or neither.

• Homework 1 - Classify the functions as even, odd, or neither: f (x) = -3x2 + 4.
• Homework 2 - It all starts after you graph the function.
• Homework 3 - This graphing example makes a nice "U" shape.

#### Practice Worksheets

Graphing them is a must!

• Practice 1 - If the graph is symmetric along the y-axis, it is classified as even.
• Practice 2 - If it is symmetric along origin (0, 0) it is classified as odd.
• Practice 3 - If the function does not meet either measure asymmetric to these tendencies, it is classified as neither.

#### Math Skill Quizzes

You should be able to recognize some trends in the graphs as you move forward.

• Quiz 1 - Is f (x)=x4 + x9 + x : even, odd, or neither?
• Quiz 2 - These mostly are symmetric about the y-axis and all the exponents are even, that makes them classified as even.
• Quiz 3 - I think that it is funny that symmetric graphs are odd. Kind of defies logic?

### Why is Classifying Functions Important at All?

As we progress forward with precalculus it is often important to understand the connection between algebra and geometry. This reminds us how the two seemingly different areas relate and how as we advance, we can transverse between these two worlds. In this case we can visualize algebraic statements and geometric statements in the form of a graph. As students start to make their way into the world of calculus, they will be able to use this skill to reduce complex integrals to zero by understanding this simple classification skill. It is something you want to know for those rainy days in calculus class.