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Range is a Function of Domain 1

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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 and Explanations

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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