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, 5th 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 

Chapter 1: Linear Functions and Change  

1.1 Functions and Function Notation
   SR: 2, 4, 7, 8, 10&
   E&P: 2, 5, 7, 9, 10, 13, 14, 16, 24, 25, 26, 28, 32, 33, 35, 42, 46

1.2 Rates of Change
   SR: 4, 8, 10  
   E&P: 4, 8, 10, 11, 12, 13, 18, 20, 22, 23, 26, 28, 31

1.3 Linear Functions
   SR: 2, 4, 6, 8  
   E&P: 2, 6, 8, 10, 12, 14, 16, 18, 20, 29, 30, 36

1.4 Formulas for Linear Functions
   SR: 4, 7, 8, 9  
   E&P: 3, 4, 8, 10, 15, 22, 27, 28, 36, 42, 46, 47, 52, 54, 59, 61

1.5 Modeling with Linear Functions
   SR: 2, 4, 7, 8, and p. 66 #24, 26, 30
   E&P: 2, 4, 8, 10, 14, 16, 18, 28, 32

1.6 Fitting linear functions to data (optional)

   E&P: 2, 4, 6, 7, 8, 9, 10, 11, 12

Chapter 2: Functions  

2.1 Input and Output

   SR: 3, 4, 6, 8  
   E&P: 1, 2, 4, 6, 10, 16, 18, 22, 26, 28, 34, 44

2.2 Domain and Range

   SR: 2, 4, 8, 10, 12 
   E&P: 4, 6, 8, 10, 12, 16, 24, 26, 30, 36, 38

2.3 Piecewise-defined functions 

   SR: 4, 8, 9, 10  
   E&P: 2, 4, 6, 10, 14, 17, 20, 24, 26, 28, 31

2.4 Preview of Transformations: Shifts 

   SR: 2, 6, 8  
   E&P: 1, 2, 4, 6, 7, 8, 9, 10, 12, 14, 16, 18, 26

2.5 Preview of Composite and Inverse Functions 

   SR: 2, 3, 4, 10, 11  
   E&P: 2, 4, 7, 8, 9, 10, 11, 13, 16, 30, 34, 40, 44, 46, 52, 56, 58  

2.6 Concavity 

   E&P: 2, 3, 4, 10, 12, 14, 16, 18, 22, 24, 26  

Chapter 3: Quadratic Functions  

3.1 Introduction to the Family of Quadratic Functions 

   SR: 4, 5, 8, 10  
   E&P: 2, 7, 9, 10, 12, 14, 20, 22, 26, 28, 32, 34, 36, 37, 42  

3.2 The vertex of a Parabola 

   SR: 2, 4, 5, 6, 8, 10  
   E&P: 1, 2, 4, 8, 10, 12, 17, 18, 28, 30, 32, 38, 40  

Chapter 6: Transformations and their graphs  

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

6.1 Shifts, reflections, and symmetry 

   SR: 6, 8, 10  
   E&P: 2, 3, 4, 8, 12, 16, 22, 24, 25, 27, 31, 32, 38, 44, 48  

6.2 Vertical stretches and compressions 

   SR: 1, 2  
   E&P: 1, 2, 4, 8, 9, 10, 11, 12, 16, 22, 28, 29, 34, 36, 37, 39 

6.3 Horizontal stretches and combinations of transformations 

   SR: 2, 4, 14, 16  
   E&P: 1, 2, 8, 10, 14, 18, 20, 25, 28, 32, 36, 41, 44, 48, 50, 52  

Chapter 11: Polynomial and Rational Functions 

11.1 Power functions and proportionality 

   SR: 2, 4, 6, 8, 10  
   E&P: 1, 5, 8, 10, 14, 18, 21, 22, 27, 32, 34, 35, 47, 52, 54, 55  

11.2 Polynomial functions 

   SR: 1, 4, 6, 8  
   E&P: 6, 8, 11, 16, 19, 22, 27, 32, 34, 36, 40, 43, 44, 46  

11.3 The short-run behavior of polynomials 

   SR: 2, 4, 5, 7  
   E&P: 2, 4, 6, 8, 9, 12, 13, 20, 26, 28, 30, 36, 44, 49  

11.4 Rational functions 

   SR: 2, 3, 4, 6, 8 
   E&P: 8, 10, 14, 16, 18, 20, 22 / 24, 27, 28, 29, 30, 32, 35  

11.5 The short-run behavior of rational functions 

   E&P: 1, 2, 4, 6, 8, 10 / 12, 14, 16, 20, 28, 31, 34, 38, 46  

 

See Course Page for additional resources.