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# Range is a Function of Domain 2

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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

Answers

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

1. Lucia can become a National Merit Scholar if her PSAT score is high.
Independent Variable(s):
Dependent Variable(s):

2. Engineers from The Department of Public Works conducted a water drainage study. They report that flooding is contingent upon the amount of trash clogging storm drains.
Independent Variable(s):
Dependent Variable(s):

3. The number of alcohol-related automobile fatalities is a function of lenient drunk-driving laws.
Independent Variable(s):
Dependent Variable(s):

4. Because a high-profile celebrity is running for governor, more people are voting in the gubernatorial election.
Independent Variable(s):
Dependent Variable(s):

5. When a woman has a career in math and science, she earns just as much money as her male counterparts.
Independent Variable(s):
Dependent Variable(s):

6. The perimeter of a rectangle is a function of the polygon’s length and width.
Independent Variable(s):
Dependent Variable(s):

7. The length and width of a parallelogram determine its area.
Independent Variable(s):
Dependent Variable(s):

8. The sale price of a sweater is a function of the original price and the discount rate.
Independent Variable(s):
Dependent Variable(s):

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