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.
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
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
Rewrite the following equations in function notation.
Why Use Function Notation?
Write functions to represent the total each friend spent at the park.
Function: A function is a relationship between two variables such that the input value has ONLY one output value.
Dependent variable: A dependent variable is one whose values depend upon what is substituted for the other variable.
Independent variable: The independent variable is the variable which is not dependent on another variable. The dependent variable is dependent on the independent variable.
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?
- Rewrite using function notation: y=56x−2.
- Rewrite using function notation: m=n2+2n−3.
- 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 x number 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 g.
- Write an inequality to represent the following: 11 minus b is at least 77.
- Find the value of the variable k:13(k)=169.