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. 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):