MAT 1100 Quantitative Reasoning: Module 3, Lesson 2, Assignment 2

This document presents a complete solution to the MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2. The assignment covers fundamental concepts of functions, including determining if a relation is a function, identifying the domain and range, and understanding function notation. The solution demonstrates how to solve for y in terms of x and represent equations using function notation. It also includes evaluating functions, finding ordered pair solutions from a graph, and graphing linear functions. Furthermore, the assignment involves real-world applications, such as writing linear functions to model scenarios like truck rental costs and electrician fees, and estimating sales based on linear trends. The solution provides detailed explanations and step-by-step calculations for each problem, ensuring a thorough understanding of the concepts.

MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2
Student Name:
1) Decide whether the relation is a function.
a) {(-8, 2), (-8, 8), (-1, 8), (5, -7), (10, -8)} A) Function B) Not a function
Solution: Note that a function is a relationship in which each input has exactly one and unique output. Since, in
ordered pair (-8, 2) and (-8, 8), the input value is -8 and output values are 2 and 8 which are not unique. Hence,
the given relation is not a function.
b)
A) Function B) Not a function
Solution: Since, each input has exactly one and unique output. So the given relation is a function.
2) Give the domain and range of the each function.
a) b) f
Domain: [-3, 3] Domain: {4, 7, 12}
Range: [2, inf] Range: {13}
3) An equation that defines y as a function of x is given.
a) Solve for y in terms of x
b) replace y with the function notation f(x).

MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2
a) 5x - 6y = 5
Solution: Given 5x - 6y = 5
Gives,
b) 2x – 5y = 4
Solution: Given 2x – 5y = 4
Gives,
4) Evaluate each function.
a) Find f(7) = 4, b) Find f(-4) = -7

MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2
5) The graph of y = f(x) is shown below. Let x = -1 and find y = f(-1) = 0
Find three ordered pair solutions by completing the table. Then use the ordered pairs to select the graph
of the equation.
6) y = 4x + 3
x y
0 3
1 7
-1 -1
A) B)
C) D)
And the graph of the function is

MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2
Hence, answer option (A) is correct.
7) A truck rental company charges $35, plus $0.07 per mile to rent a moving truck for a day. If x represents the
number of miles driven and f(x) represents the total cost to rent the truck for a day, write a linear function that
models the situation.
Solution: The linear function is , where x is miles driven
8) An electrician charges a fee of $60 plus $45 per hour. Let C(x) is the cost in dollars of using the electrician
for x hours. Write a cost function.
Solution: The cost function is
9) Assume that the sales of a computer retail store are approximated by a linear function. Sales were in
1985 and in 1990. Let x = 0 represent 1985
a) Find the equation giving yearly sales.
b)Estimate sales in 1993.
Solution (a): Let and . Then the equation of linear function is
Solution (b): Estimate sales in x = 1993 is

MAT 1100 Quantitative Reasoning Module 3 Lesson 2 Assignment 2
10) Graph the linear function. Give the domain and range
f(x) = -5x + 4
A) D = (-∞, ∞), B) D = (-∞, ∞),
R = (-∞, ∞) R = (-∞, ∞)
Solution: The graph of the function f(x) = -5x + 4 is
B) D = (-∞, ∞), R = (-∞, ∞)