Loyola University Chicago

Mathematics and Statistics

MATH 117: Precalculus I

Course Details
Credit Hours: 3
Prerequisites: MATH 100 with a grade of C- or higher, or Math Placement Assessment.
Description:  The study of functions, their graphs, and their basic properties. Emphasis is placed on polynomial functions, including linear and quadratic functions. Computing real and complex roots of polynomials is explored. Additional topics include: the study of rational functions, absolute value functions, and inverse functions; and solutions of systems of equations.

Functions Modeling Change: A Preparation for Calculus, 6th Edition, Eric Connally, Deborah Hughes-Hallett, Andrew M. Gleason packaged with WileyPlus.

Chapter 1: Linear Functions and Change 

   1.1 Functions and Function Notation 
   1.2 Rates of Change 
   1.3 Linear Functions 
   1.4 Formulas for Linear Functions 
   1.5 Modeling with Linear Functions 
   1.6 Fitting linear functions to data 

Chapter 2: Functions 

   2.1 Input and Output 
   2.2 Domain and Range 
   2.3 Piecewise-defined functions 
   2.4 Preview of Transformations: Shifts 
   2.5 Preview of Composite and Inverse Functions 
   2.6 Concavity 

Chapter 3: Quadratic Functions 

   3.1 Introduction to the Family of Quadratic Functions 
   3.2 The vertex of a Parabola 

Chapter 6: Transformations and their graphs 

   6.1 Shifts, reflections, and symmetry 
   6.2 Vertical stretches and compressions 
   6.3 Horizontal stretches and combinations of transformations 

Chapter 11: Polynomial and Rational Functions 

   11.1 Power functions and proportionality 
   11.2 Polynomial functions 
   11.3 The short-run behavior of polynomials 
   11.4 Rational functions 
   11.5 The short-run behavior of rational functions 

Abbreviations:

S=Skills Review, E=Exercises, GTP=Go Tutorial, AQ=Additional Questions, RE=Review Exercises, CTQ=ConceptTest Question

 

Chapter 1: Linear Functions and Change

1.1 Functions and Function Notation
      S: 5, 8
      E: 1, 5, 7, 9. 10, 13, 14, 17, 23, 29, 33, 35, 36, 38, 46, 50b

1.2 Rates of Change
      S: 4, 9
      E: 8, 13, 14, 18, 22, 32, 35a, 37ab

1.3 Linear Functions
      S: 1, 3, 6, 14
      E: 2, 6, 8, 10, 13, 17, 18, 28, Chapter 1 RE16, Chapter 1 RE 37,

      Chapter 1 RE 36ab, GTP 29

1.4 Formulas for Linear Functions
      S: 4, 9
      E: 3, 6, 8, 12, 15, 29, 32, 33, 39, 40, 44, 47, 50ab, 55, 58ab, 59, 65,

      GTP 60

1.5 Graphs and Models with Linear Functions and Inequalities
      S: 1, 5
      E: 1, 3, 7, 9, 14, 17, 22, 23, 25, 36

1.6 Fitting Linear Functions to Data (optional)
      E: 2, 5, 7, 9, 11

 

Chapter 2: Functions

2.1 Input and Output
      S: 5, 14
      E: 2, 4, 9, 10, 11, 14, 18, 22, 23, 29, 33, 49

2.2 Domain and Range
      S: 2, 11
      E: 1, 6, 7, 13, 15, 24, 26, 29, 36, GTP 15

2.3 Piecewise-Defined functions
      S: 5, 12
      E: 3, 4, 6, 9, 13, 15, 20, 22, 25abc, 26, 28, 31

2.4 Preview of Transformations: Shifts
      E: 1, 7, 8, 9, 11, 13, 14, 16, 21, 26

2.5 Preview of Composite and Inverse Functions
      S: 3, 8, 10
      E: 1, 2, 7, 8, 12, 18, 23, 25, 29, 32, 33, 35, 37, 44, 46, 54, 67, 72,
          75, 82, GTP 70, GTP 83

2.6 Concavity
      E: 1, 3, 4, 7, 8, 10, 12, 17, 18, 27, 28, 32, 33, 35, 36, 39

 

Chapter 3: Quadratic Functions

3.1 Introduction to the Family of Quadratic Functions
      S: 1, 10, 17
      E: 3, 5, 9, 12, 13, 14, 24, 26, 29, 30, 32, 35, 37, 42ab

3.2 The Vertex of a Parabola
      S: 3, 8
      E: GTP 13, 3, 9, 10, 13, 28, 29, 31, 39, 40

 

Chapter 6: Transformations and Their Graphs

(Skip any problems in this chapter using exponential or logarithmic functions.)

6.1 Shifts, Reflections, and Symmetry
      S: 9
      E: 3, AQ 5, GTP 7, 8, 14, 15, 16, 21, 22, 23, 24, 25, 27, 32, 38a, 44

6.2 Vertical Stretches and Compressions
      S: 2, 3
      E: 1, 2, 4, 7acf, 13, 16, 19, 22, 25, 27, 28, 29, 35, 36, 37, 39

6.3 Horizontal Stretches and Combinations of Transformations
      S: 6, 16
      E: 1, 2, 8, 10, 14, 15ab, GTP 15c, 17, 20, 25, 29, 30, 31, 32, 33, 34,

      35, 36, 42, 45, 48, 52 (multipart version in WileyPlus), 55, 56

 

Chapter 11: Polynomial and Rational Functions

11.1 Power Functions and Proportionality
      S: 3, 5, 12
      E: 1, 5, 8, 9, 10, 11, 12, 14, 15, 18, 22, 23, 26, 32, 37, 42

11.2 Polynomial Functions and Their Behavior
      E: 4, 6, 7, 11, 20, CTQ 3, 21, GTP 26, 33, 34, 35, 36, 38, 40, 41,

      GTP 43, 44

11.3 Zeros of Polynomials and Short-Run Behavior
      E: AQ 1, 3, 6, 17, GTP 19, 21, 23, 31, 34, 36, 41, 47,

      Chapter 11 RE 63

11.4 Rational Functions
      S: 3, 9, 13
      E: 3, 9, 11, 13, 14, 15, 16, 19, 23, 24, 25, 26, GTP 27, 29, 31a

11.5 The Short-Run Behavior of Rational Functions
      E: 2, 5, 8, 9, 11, 12, 14, 17, 20, 26, 27, 37, 39, 46, 51, 52, CTQ 7

Math 117 Common Final Study Materials 

The Math 117 common final exam is scheduled for Wednesday, December 15, 2021, 8:00 pm – 10:00 pm.  Calculators will be permitted on the exam, however devices with a CAS (computer algeabra system) will not be permitted during the exam.  We provide a sample exam and study materials here from the 2020-2021 academic year.  Please note that these exams were administered online.  We plan for the Fall 2021 final exam to be administered in person on the Loyola campus.   

We provide two pdf files: 

  1. MATH 117 Exam questions from Fall 2020 
  2. MATH 117 Final exam practice problems

See Course Page for additional resources.