• Share
Send to a Friend via Email

### Your suggestion is on its way!

An email with a link to:

was emailed to:

Thanks for sharing About.com with others!

You can opt-out at any time. Please refer to our privacy policy for contact information.

Discuss in my forum

# Range is a Function of Domain 3 Answers

A function is a set of data that has one distinct output for each input. Graphs, charts, equations, and verbal descriptions – these depict functions. This article teaches how to look at a verbal description of a function and identify the input and output.

### Other Terms for Input and Output

Input
•    x-value
•    independent variable
•    independent quantity
•    domain
•    cause
•    action

Output
•    y-value
•    dependent variable
•    dependent quantity
•    range
•    effect
•    consequence

### Example of Input and Output

As you have probably surmised, you control the input. Once the input travels through a function, you get your output. OK, I’m a big math nerd, but I will leave Algebra land to explain.

Imagine that you’re running late for math tutoring. You’re speeding 60 miles per hour in a 20 mile per hour school zone. A cop pulls you over and writes you a \$300 speeding ticket. Let’s break down this real world cause and effect situation.

Input: You chose to exceed the speed limit by 40 miles per hour.
Output: You received a speeding ticket.

You see, you can control how fast you’re going, but the consequence, or the output, is up to the cop.

### Find the Independent and Dependent Variables in Verbal Descriptions

Sometimes you’ll see this statement:

_______________ is a function of __________________.

When you see that, think:

Dependent variable is a function of Independent variable.

Example: The number of close friends that Halitosa has is a function of her level of personal hygiene.
Independent variable(s): Halitosa's level of personal hygiene
Dependent variable(s):  Number of close friends

### Exercises

Instructions:  Determine the independent and dependent variables in the following situations:

1. The number of people remaining in Houston during a hurricane evacuation is a function of the number of people who flee the city.
Independent Variable(s):  Number of people who flee the city
Dependent Variable(s): Number of people remaining in the city

2. The steepness of a linear function is a function of the slope of the line. Consider two lines: one has a slope of 10, the other, 3. The line with a slope of 10 is steeper.
Independent Variable(s): Slope of a line
Dependent Variable(s): Steepness of a line

3. The length, width, and height of a rectangular prism determine the object’s volume.
Independent Variable(s): Length, width, and height of a rectangular prism
Dependent Variable(s): Volume of a rectangular prism

4. The sum of the angle measurements of a polygon depends on its number of sides. For example, a triangle has 3 sides. Therefore, the sum of its angle measurements is 180°.
Independent Variable(s): The number of sides of a polygon
Dependent Variable(s): The sum of a polygon's angle measurements

5. The area of a circle is a function of its diameter.
Independent Variable(s):  The diameter of a circle
Dependent Variable(s): The area of a circle

6. The circumference of a circle is a function of its radius.
Independent Variable(s): The radius of a circle
Dependent Variable(s): The circumference of a circle

7. A right triangle has 3 sides: 2 legs and 1 hypotenuse. The area of the right triangle is a function of the lengths of the 2 legs.
Independent Variable(s): The lengths of the legs
Dependent Variable(s): The area of the right triangle

8. The costs of a cheeseburger and a medium order of fries depend on the menu price and the sales tax rate.
Independent Variable(s): Menu price and sales tax rate
Dependent Variable(s): Costs of a cheesburger and medium order of fries

Explore Mathematics