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 \(C(x)=30x\).

A:

20

B:

30

C:

50

D:

90

E:

100

Problem 2

A rectangle has an area of 24 cm2. 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 \(y=x^3\).

A:

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

B:

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

C:

\((3, 9)\)

D:

\((\frac12, \frac18)\)

E:

\((4, 64)\)

F:

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

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.

  1. Identify all numbers that make sense as inputs and outputs for this function.
  2. Sketch a graph of \(B\).
Horizontal axis, people riding the bus. Scale 0 to 12, by 2's. Vertical axis, earnings in dollar. Scale 0 to 40, by 10's. 

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.

A:

\(f(3)>0\)

B:

\(f(3)>5\)

C:

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

D:

\(g(\text-1)

E:

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

(From Unit 4, Lesson 5.)

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 \(f\).

(From Unit 4, Lesson 3.)

Problem 7

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

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

Function on coordinate plane.

​​​​​

(From Unit 4, Lesson 6.)

Problem 8

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

Show A

10 data points on coordinate plane.

Show C

10 data points on coordinate plane.

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.

(From Unit 4, Lesson 9.)