## Comparing Properties of Two Functions

#### Aligned To Common Core Standard:

**Grade 8 Functions** - 8.F.A.2

How to Compare the Properties of Two Functions A function is a concept which needs to be adequately understood so that it doesn't create problems in the future. Most students might not know that functions will e difficult as you move to higher classes. There are three ways to compare functions, i.e., algebraically, numerically, and graphically. Let us compare two functions numerically. Let us consider an example of y=3x+5. In this example, y is a dependent of x, so in other words, if we keep on changing the value of x, then y will increase as well. Let's look at the table as an example. x, y = (-1, 2), (0, 5), (4, 17), (-5, -10) In the table above, it is visible that different values of x change the values of y. For instance, if we put the value -1 in the equation. Then the value of y becomes 2. It means that the value of y depends on the value of x. These worksheets and lessons teach students how to compare the various properties of functions.

### Printable Worksheets And Lessons

- Compare the Functions
Step-by-Step Lesson- You are provided two functions in equation
and table form. Compare them as best you can.

- Guided Lesson
- We look at positive and negative slope and what it means about
the relationship between the two functions.

- Guided Lesson Explanation
- These problems involve a great deal of slope calculations. Make
sure your students have that skill down pat before moving on to
this skill.

- Independent Practice
-Not only are the problems themselves lengthy, the answers take
up a great deal of paper to solve.

- Matching Worksheet
- Solve all the word problems to find their match. This one only
has 4 problems because of the sheer volume the problems take up.

- Co Functions Worksheet Five
Pack - This pack and the next is here to show you the next level
of material that is coming up for this topic.

- Composition of Functions Worksheet Five Pack - This really boils down to the old plug the numbers in and solve type of problem.

#### Homework Sheets

Compare the functions and the input/output charts for slope.

- Homework 1 - The equation of straight line is y = mx +b Slope is the rate of change. The coefficient of x is the slope of the line.
- Homework 2 - Compare the two linear functions listed below and determine which has a negative slope.
- Homework 3 - Will is a shop keeper. He has 25 toys at the start of the day. He sold 5 toys per day. Write the rule for the total number of sold toys as a function of the number of days (d). c = 25 - 5d

#### Practice Worksheets

This is a skill that covers a lot of ground and can be interpreted many different ways.

- Practice 1 - Roy starts with $100. He spends $10 per week. Let y be the amount remaining as a function of the number of weeks, x.
- Practice 2 - Determine which has the greater rate of change.
- Practice 3 - Compare the following functions to determine which has the greater rate of change.

#### Math Skill Quizzes

The variable g(x) is introduced and sometimes it will make the kids' heads' spin