# Domain and Range of Functions Worksheets

What are the Domains and Ranges of Functions? You might have because mathematics is filled with such words. Much as these words are intimidating, they entail a lot of meaning to it. The domain of a function refers to the set of possible values of the independent variable. The domain is the set of all possible x-values, which will, when applied to the y-variable, will make the function work. When discovering the domain, bear in mind: The denominator (bottom) of a fraction shouldn't be zero. The number under the sign of square root must be positive in this section. The domain of a rational function consists of all the real numbers except the denominator. The range, on the other hand, is the complete set of all likely results of the dependent variable (y usually) after we have substituted the domain. The range is a set of values of the dependent variable that are a result of inserting the domain values into a function. To put it simply, the definition means: The resulting y-values you get after substituting the x-values in an equation.

### Aligned Standard: HSF-IF.A.2

- Which Range Fits Step-by-step Lesson- You are given a graph and asked to determine an acceptable range for it.
- Guided Lesson - See if you can determine the acceptable ranges of these functions.
- Guided Lesson Explanation - We quickly learn to accept all the possible y-values and go from there.
- Practice Worksheet - We use to call these "Home on the Range" problems. See if you get what we mean.
- Matching Worksheet - Match the ranges with the graphs. We also give you multiple choices.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

We focus solely on range. This is because many teachers tell us that their is where the need is.

- Homework 1 - The range of a function is the set of all possible y-values. The largest y-value on the graph appears at the vertex where y is mentioned by the formula.
- Homework 2 - So, the range is the set of all real numbers. Let's see that on a graph and make sense of it.
- Homework 3 - What is the range of this function? a {y | y ≤ 4}, b {y | y ≥ 4}, c {all real numbers}, d {y | y <4}

### Practice Worksheets

You should see a brand new section on range to follow this shortly.

- Practice 1 - This is one nice solid problem for you. A complete explanation is provided for you.
- Practice 2 - When do you want to range this function out? This line jumps quadrants.
- Practice 3 - You will need to count the lines here. This one is really large.

### Math Skill Quizzes

Multiple choice is the common method used to assess this skill.

- Quiz 1 - The domains is the set of all the inputs. We are focused on determining the possible outputs.
- Quiz 2 - Some much larger values here. Use the values to get you going.
- Quiz 3 - Scale this back to complete the values here.

### How Does This Skill Apply to The Real World?

Functions are used to model mathematical systems that involve an input and an output. They are used in types of rule based mathematical patterns. If you go to any vending machine you would be using a rules based math system to make your purchase. Each coin you input results in validated outcome, once you put enough coins in to satisfy the output of the cost of the item that you choose, your purchase is complete. The bag of chips, bottle of water, of tasty treat will land to the bottom of the machine. Using our example of the vending machine we can see that the coins are the values that determine the domain. Assuming we the machine only accepts common coins, domain would be 1 (penny), 5 (nickel), 10 (dime), and 25 (quarter). The range is all the possible output values. In the sense of the vending machine the range would be the cost of all of the products that are available in the vending machine. You will find this skill to lend itself to just about any financial mathematical system like gas pumps and even street crossing signals. These measures are very helpful to understand the stress a system can contain and all of the possibilities that are available when you use it.

There are many circumstances where understanding these two factors can be critical. Having an understanding of what can be input and what the possible consequences of those inputs are allows people to make decision to help navigate towards one of the better perceived outcomes. This is what happens on missions to space all the time. Engineers constantly are evaluating all possible variables and how they will affect the rocket or space shuttle. When something unexpected occurs they must evaluate what possible choices they have and what outcomes those choices will have. Business leaders do this all the time too, they need to first understand what outcome they are trying to achieve. Then they need to see all of the choices that have presented themselves. From there they need to do their best to understand which choice will lead them to the outcome that they are hopeful for.