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# Function Notation

## Explore f(x) notation for functions

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Practice Function Notation
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Estimated18 minsto complete
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Function Notation

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.

### Guidance

#### Example C

Write functions to represent the total each friend spent at the park.

Solution:

J(r)=2r\begin{align*}J(r)= 2r\end{align*} represents Joseph’s total,

L(r)=2r\begin{align*}L(r)= 2r\end{align*} represents Lacy's total,

K(r)=2r\begin{align*}K(r)= 2r\end{align*} represents Kevin's total, and

A(r)=2r\begin{align*}A(r)= 2r\end{align*} represents Alfred’s total.

### Guided Practice

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 100+7x\begin{align*} 100+7x\end{align*} and for the revenue, we had the expression 15x\begin{align*} 15x\end{align*} , where x\begin{align*}x\end{align*} is the number of shirts.

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? Solution: a. The cost function we will write as C(x)=100+7x\begin{align*}C(x)=100+7x\end{align*} and the revenue function we will write as R(x)=15x\begin{align*}R(x)=15x\end{align*} . b. Since C(x)\begin{align*}C(x)\end{align*} represents the costs, we substitute in800 for C(x)\begin{align*}C(x)\end{align*} and replace the equation with the appropriate inequality symbol

100+7x800

This reads that 100+7x\begin{align*}100+7x\end{align*} is less than or equal to $800, so we have written the inequality correctly. c. We substitute in$1500 for R(x)\begin{align*}R(x)\end{align*} , getting

1500=15x.\begin{align*}1500=15x.\end{align*}

d. We want to find the value of x\begin{align*}x\end{align*} that will make this equation true. It looks like 100 is the answer. Checking this we see that 100 does satisfy the equation. The students must sell 100 shirts in order to have a revenue of 1500. 1500=15(100)\begin{align*}1500=15(100)\end{align*} 1500=1500\begin{align*}1500=1500\end{align*} ### Practice 1. Rewrite using function notation: y=56x2\begin{align*}y= \frac{5}{6} x-2\end{align*} . 2. Rewrite using function notation: m=n2+2n3\begin{align*}m=n^2+2n-3\end{align*} . 3. What is one benefit of using function notation? 4. Write a function that expresses the money earned after working some number of hours for10 an hour.
5. Write a function that represents the number of cuts you need to cut a ribbon in x\begin{align*}x\end{align*} number of pieces.
6. 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.

Mixed Review

1. Compare the following numbers 23  21.999\begin{align*}23 \ \underline{\;\;\;\;\;} \ 21.999\end{align*} .
2. Write an equation to represent the following: the quotient of 96 and 4 is g\begin{align*}g\end{align*} .
3. Write an inequality to represent the following: 11 minus b\begin{align*}b\end{align*} is at least 77.
4. Find the value of the variable k:13(k)=169\begin{align*}k:13(k)=169\end{align*} .

### Vocabulary Language: English Spanish

dependent variable

dependent variable

A dependent variable is one whose values depend upon what is substituted for the other variable.
Function

Function

A function is a relation where there is only one output for every input. In other words, for every value of $x$, there is only one value for $y$.
independent 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.