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
• independent variable
• independent quantity
• dependent variable
• dependent quantity
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
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