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# Range is a Function of Domain 1

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. A high SAT score is a function of rigorous test preparation and strong math, writing, and reading skills.
Independent Variable(s):
Dependent Variable(s):

2. The harder Amy presses on the gas pedal, the more her car accelerates.
Independent Variable(s):
Dependent Variable(s):

3. Webster Strunk has no clue why his credit card bill is so high, so he tracks his monthly expenses. He learns that he spends \$1,200 per month at restaurants. He only makes \$1,105 a month, so he charges his excess expenses to his credit card.
Independent Variable(s):
Dependent Variable(s):

4.  The amount Joan owes on her department store credit card is a function of how much she spends at the store and the credit card's interest rate and annual fee.
Independent Variable(s):
Dependent Variable(s):

5. Uncertainty is a function of the number of choices available.
Independent Variable(s):
Dependent Variable(s):

6. The monthly cost to use a cell phone bill is a function of the type of cell phone and text message package.
Independent Variable(s):
Dependent Variable(s):

7.  The residents of Norman Meadows want to build a tunnel that connects their township to Norman Heights. Completion of the tunnel, which will depend on tax revenues, will reduce traffic congestion.
Independent Variable(s):
Dependent Variable(s):

8. Hair color is a function of age, genetic makeup, and proximity to a colorist.
Independent Variable(s):
Dependent Variable(s):

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