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 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 \(y=x^3\).
\((\text{-}1, \text{-}1)\)
\((\text{-}2, 8)\)
\((3, 9)\)
\((\frac12, \frac18)\)
\((4, 64)\)
\((1, \text{-}1)\)
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.
\(f(3)>0\)
\(f(3)>5\)
\(g(\text-1)=0.8\)
\(g(\text{-}1)<f(\text{-}1)\)
\(f(0)=g(0)\)
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.
Show A
Show C
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.