Suppose that you want to set up a function that allows you to input a dog's age in human years and which outputs the dog's age in dog years. How would you go about setting up such a function, and what notation would you use? Would the notation be the same as it was for the equations that you've looked at in previous Concepts? In this Concept, you'll learn what is needed to write a function such as this.
Instead of purchasing a one-day ticket to the theme park, Joseph decided to pay by ride. Each ride costs $2.00. To describe the amount of money Joseph will spend, several mathematical concepts can be used.
First, an expression can be written to describe the relationship between the cost per ride and the number of rides,
Using Joseph’s situation, write the following:
a. An expression representing his total amount spent
b. An equation representing his total amount spent
c. An equation that shows Joseph wants to spend exactly $22.00 on rides
d. An inequality that describes the fact that Joseph will not spend more than $26.00 on rides
The variable in this situation is the number of rides Joseph will pay for. Call this
In addition to an expression, equation, or inequality, Joseph’s situation can be expressed in the form of a function or a table.
Definition: A function is a relationship between two variables such that the input value has ONLY one output value.
Writing Equations as Functions
A function is a set of ordered pairs in which the first coordinate, usually
Consider Joseph’s equation
Rewrite the following equations in function notation.
a. According to the definition of a function,
b. This time the dependent variable is
Why Use Function Notation?
Why is it necessary to use function notation? The necessity stems from using multiple equations. Function notation allows one to easily decipher between the equations. Suppose Joseph, Lacy, Kevin, and Alfred all went to the theme park together and chose to pay $2.00 for each ride. Each person would have the same equation
Write functions to represent the total each friend spent at the park.
Recall the example from a previous Concept where a student organization sells shirts to raise money. The cost of printing the shirts was expressed as
a. Write two functions, one for the cost and one for revenue.
b. Express that the cost must be less than or equal to $800.
c. Express that the revenue must be equal to $1500.
d. How many shirts must the students sell in order to make $1500?
a. The cost function we will write as
This reads that
c. We substitute in $1500 for
d. We want to find the value of
Rewrite using function notation:
Rewrite using function notation:
- What is one benefit of using function notation?
- Write a function that expresses the money earned after working some number of hours for $10 an hour.
Write a function that represents the number of cuts you need to cut a ribbon in
xnumber of pieces.
- Jackie and Mayra each will collect a $2 pledge for every basket they make during a game. Write two functions, one for each girl, expressing how much money she will collect.
Compare the following numbers
23 −−− 21.999.
Write an equation to represent the following: the quotient of 96 and 4 is
Write an inequality to represent the following: 11 minus
bis at least 77.
Find the value of the variable