# Lesson 10

Domain and Range (Part 1)

Let’s find all possible inputs and outputs for a function.

### Problem 1

The cost for an upcoming field trip is $30 per student. The cost of the field trip \(C\), in dollars, is a function of the number of students \(x\).

Select **all **the possible outputs for the function defined by \(C(x)=30x\).

20

30

50

90

100

### Problem 2

A rectangle has an area of 24 cm^{2}. Function \(f\) gives the length of the rectangle, in centimeters, when the width is \(w\) cm.

Determine if each value, in centimeters, is a possible input of the function.

- 3
- 0.5
- 48
- -6
- 0

### Problem 3

Select **all **the possible input-output pairs for the function \(y=x^3\).

\((\text{-}1, \text{-}1)\)

\((\text{-}2, 8)\)

\((3, 9)\)

\((\frac12, \frac18)\)

\((4, 64)\)

\((1, \text{-}1)\)

### Problem 4

A small bus charges $3.50 per person for a ride from the train station to a concert. The bus will run if at least 3 people take it, and it cannot fit more than 10 people.

Function \(B\) gives the amount of money that the bus operator earns when \(n\) people ride the bus.

- Identify all numbers that make sense as inputs and outputs for this function.
- Sketch a graph of \(B\).

### Problem 5

Two functions are defined by the equations \(f(x)=5-0.2x\) and \(g(x)=0.2(x+5)\).

Select **all** statements that are true about the functions.

\(f(3)>0\)

\(f(3)>5\)

\(g(\text-1)=0.8\)

\(g(\text-1)

\(f(0)=g(0)\)

### Problem 6

The graph of function \(f\) passes through the coordinate points \((0,3)\) and \((4,6)\).

Use function notation to write the information each point gives us about function \(f\).

### Problem 7

Match each feature of the graph with the corresponding coordinate point.

If the feature does not exist, choose “none”.

### Problem 8

The graphs show the audience, in millions, of two TV shows as a function of the episode number.

For each show, pick two episode numbers between which the function has a negative average rate of change, if possible. Estimate the average rate of change, or explain why it is not possible.