PreCalculus Curriculum Guide
Text: Precalculus. 6th Edition, Houghton Mifflin, Larson-Hostetler.
Instructional Usage:
1. The text, homework problems, quizzes, tests.
2. Overhead projector, Elmo, computer software, websites specific to chapter
information and Youtube demonstrations
3. Usage of a Graphing Calculator
Chapter Summary
Chapter 1: Functions and Their Graphs
1.1 Graphs of Equations
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Sketch graphs of equations
Find x- and y- intercepts of graphs of equations
Use symmetry to sketch graphs of equations
Find equations and sketch graphs of circles
Use graphs of equations in solving real-life problems
1.2 Linear Equations in Two Variables
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Use slope to graph linear equations in two variables
Find slopes of lines
Write linear equations in two variables
Use slope to identify parallel and perpendicular lines
Use linear equations in two variables to model and solve real-life problems
1.3 Functions
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Determine whether relations between two variables are functions
Use function notation and evaluate functions
Find the domains of functions
Use functions to model and solve real-life problems
Math 136 Ivy Tech – 1st semester
1.4 Analyzing Graphs of Functions
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Use the Vertical Line Test for functions
Find the zeros of functions
Determine intervals on which functions are increasing or decreasing
Identify even and odd functions
1.5 A Library of Functions
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Identify and graph linear and squaring functions
Identify and graph cubic, square root, and reciprocal functions
Identify and graph step and other piecewise-defined functions
Recognize graphs of common functions
1.6 Shifting, Reflecting, and Stretching Graphs
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Use vertical and horizontal shifts to sketch graphs of functions
Use reflections to sketch graphs of functions
Use nonrigid transformations to sketch graphs of functions
1.7 Combinations of Functions
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Add, subtract, multiply, and divide functions
Find the composition of one function with another function
Use combinations of functions to model and solve real-life problems
1.8 Inverse Functions
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Find inverse functions informally and verify that two functions are inverse
functions of each other
Use graphs of functions to determine whether functions have inverse functions
Use the Horizontal Line Test to determine if functions are one-to-one
Find inverse functions algebraically
1.9 Mathematical Modeling
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Use mathematical models to approximate sets of data points
Write mathematical models for direct variation
Write mathematical models for direct variation as an nth power
Write mathematical models for inverse variation
Write mathematical models for joint variation
Use the regression feature of a graphing utility to find the equation of a least
squares regression line
Math 136 Ivy Tech – 1st semester
Chapter 2: Polynomial and Rational Functions
2.1 Quadratic Functions
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Analyze graphs of quadratic functions
Write quadratic functions in standard form and use the results to sketch graphs of
functions
Use quadratic functions to model and solve real-life problems
2.2 Polynomial Functions of Higher Degree
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Use transformations to sketch graphs of polynomial functions
Use the Leading Coefficient Test to determine the end behavior of graphs of
polynomial functions
Use zeros of polynomial functions as sketching aids
Use the Intermediate Value Theorem to help locate zeros of polynomial functions
2.3 Polynomial and Synthetic Division
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Use long division to divide polynomials by other polynomials
Use synthetic division to divide polynomials by binomials of the form (x-k)
Use the Remainder Theorem and the Factor Theorem
2.4 Complex Numbers
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Use the imaginary unit I to write complex numbers
Add, subtract, and multiply complex numbers
Use complex conjugates to write the quotient of two complex numbers in standard
form
Find complex solutions of quadratic equations
2.5 Zeros of Polynomial Functions
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Use the Fundamental Theorem of Algebra to determine the number of zeros of
polynomial functions
Find rational zeros of polynomial functions
Find conjugate pairs of complex zeros
Find zeros of polynomials by factoring
Use Descarte’s Rule of Signs and Upper and Lower Bound Rules to find zeros of
polynomials
Math 136 Ivy Tech – 1st semester
2.6 Rational Functions
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Find the domains of rational functions
Find the horizontal and vertical asymptotes of graphs of rational functions
Analyze and sketch graphs of rational functions
Sketch graphs of rational functions that have slant asymptotes
Use rational functions to model and solve real-life problems
2.7 Partial Fractions
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Recognize partial fraction decompositions of rational expressions
Find partial fraction decompositions of rational expressions
Chapter 3: Exponential and Logarithmic Functions
3.1 Exponential Functions and Their Graphs
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Recognize and evaluate exponential functions with base a
Graph exponential functions
Recognize and evaluate exponential functions with base e
Use exponential functions to model and solve real-life applications
3.2 Logarithmic Functions and Their Graphs
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Recognize and evaluate logarithmic functions with base a
Graph logarithmic functions
Recognize and evaluate natural logarithmic functions
Use logarithmic functions to model and solve real-life applications
3.3 Properties of Logarithms
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Use the change-of –base formula to rewrite and evaluate logarithmic expressions
Use properties of logarithms to evaluate or rewrite logarithmic expressions
Use properties of logarithms to expand or condense logarithmic expressions
Use logarithmic functions to model and solve real-life applications
3.4 Exponential and Logarithmic Equations
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Solve simple exponential and logarithmic equations
Solve more complicated exponential equations
Solve more complicated logarithmic equations
Use exponential and logarithmic equations to model and solve real-life
applications
Math 136 Ivy Tech – 1st semester
3.5 Exponential and Logarithmic Models
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Recognize the 5 most common types of models involving exponential and
logarithmic functions
Use exponential growth and decay functions to model and solve real-life
problems
Use Gaussian functions to model and solve real-life problems
Use logistic growth functions to model and solve real-life problems
Use logarithmic functions to model and solve real-life problems
Chapter 7: Systems of Equations and Inequalities
7.1 Solving Systems of Equations
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Use the method of substitution to solve systems of equations in two variables
Use a graphical approach to solve systems of equations in two variables
Use systems of equations to model and solve real-life problems
7.2 Two-Variable Linear Systems
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Use the method of elimination to solve systems of linear equations in two
variables
Interpret graphically the numbers of solutions of systems of linear equations in
two variables
Use systems of equations in two variables to model and solve real-life problems
7.3 Multivariable Linear Systems
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Use back-substitution to solve linear systems in row-echelon form
Use Gaussian elimination to solve systems of linear equations
Solve nonsquare systems of linear equations
Use systems of linear equations in three or more variables to model and solve
application problems
7.4 Systems of Inequalities
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Sketch the graphs of inequalities in two variables
Solve systems of inequalities
Use systems of inequalities in two variables to model and solve real-life problems
7.5 Linear Programming
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Solve linear programming problems
Use linear programming to model and solve real-life problems
Math 136 Ivy Tech – 1st semester
Chapter 8: Matrices and Determinants
8.1 Matrices and Systems of Equations
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Write a matrix and identify its order
Perform elementary row operations on matrices
Use matrices and Gaussian elimination to solve systems of linear equations
Use matrices and Gauss-Jordan elimination to solve system of linear equations
8.2 Operations with Matrices
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Decide whether two matrices are equal
Add and subtract matrices and multiply matrices by real numbers
Multiply two matrices
Use matrix operations to model and solve real-life problems
8.3 The Inverse of a Square Matrix
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Verify that two matrices are inverses of each other
Use Gauss-Jordan elimination to find the inverses of matrices
Use a formula to find the inverses of 2-by-2 matrices
Use inverse matrices to solve systems of linear equations
8.4 The Determinant of a Square Matrix
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Find the determinants of 2-by-2 matrices
Find minors and cofactors of square matrices
Find the determinants of square matrices
8.5 Applications of Matrices and Determinants
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Use Cramer’s Rule to solve systems of linear equations
Use determinants to find the areas of triangles
Use a determinant to test for collinear points and find an equation of a line
passing through two points
Use matrices to code and decode messages
Math 136 Ivy Tech – 1st semester