Lesson 10

Domain and Range (Part 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 Solution For access, consult one of our IM Certified Partners. 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 Solution For access, consult one of our IM Certified Partners. 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: $$(1, \text{-}1)$$ Solution For access, consult one of our IM Certified Partners. 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 $$B$$.

Solution

For access, consult one of our IM Certified Partners.

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:

$$g(\text{-}1)<f(\text{-}1)$$

E:

$$f(0)=g(0)$$

Solution

For access, consult one of our IM Certified Partners.

(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 $$f$$.

Solution

For access, consult one of our IM Certified Partners.

(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”.

​​​​​

Solution

For access, consult one of our IM Certified Partners.

(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.

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.

Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 9.)