MTH:160 COLLEGE ALGEBRA WITH CALCULATOR
OBJTECTIVES
The student will be able to:
CHAPTER 1 GRAPHS, FUNCTIONS, AND MODELS
1.1 FUNCTIONS, GRAPHS,AND GRAPHERS
Determine whether a correspondence or a relation is a function.
Find function values, or outputs, using a formula.
Find the domain and the range of a function.
Determine whether a graph is that ofa function.
Solve application problems using functions.
1.2 FUNCTIONS ANDAPPLICATIONS
Find zeros of functions.
Graph functions, looking for intervals on which the function is increasing, decreasing, or constant, and determine relative maxima and minima.
Graph functions defined piecewise.
Given an application, find a function formula that models the application; find the domain of the function and function values, and then graph the function.
1.3 LINEARFUNCTIONS AND APPLICATIONS
Graph linear functions and equations, finding the slope and the y-intercept.
Determine equations of lines.
Solve applied problems involving linear functions.
1.4 DATAANALYSIS,CURVE FITTING, AND LINEAR REGRESSION
Analyze a set of data to determine whether it can be modeled by a linear function.
Fit a regression line to a set of data; then use the linear model to make predictions.
1.5 DISTANCE, MIDPOINTS, AND CIRCLES
Find the distance between two points in the plane and the midpoint of a segment.
Find an equation of a circle with a given center and radius, and given an equation of a circle, find the center and the radiuis.
Graph equations ofcircles.
1.6 SYMMETRY
Determine whether a graph is symmetric with respect to the x-awis, the y-axis, and the origin.
Determine whether a function is even, odd, or neither even nor odd.
1.7 TRANSFORMATIONS OF FUNCTIONS
Given the graph of a function, graph its transformation under translations, reflections, stretchings, and shrinkings.
1.8 THE ALGEBRA OF FUNCTIONS
Compute function values forthe sum, the difference, the product, and the quotient of two functions, and determine the domains.
Find the composition of two functions and the domain of the composition; and decompose a function as a composition of two functions.
5.1 THE PARABOLA
Given an equation of a parabola, complete the square, if necessary, and then find the vertex, the focus, and the directrix and graph the parabola.
TEST
CHAPTER 2. POLYNOMIAL AND RATIONAL FUNCTIONS
2.1 INTRODUCTIONTO POLYNOMIAL FUNCTIONS AND COMPLEX NUMBERS
Use a grapher to graph a polynomial fUnction and find its real-number zeros, relative maximum and minimum values, and domain and range.
Perform computations involving complex numbers.
2.2 QUADRATIC EQUATIONS AND FUNCTIONS
Solve quadratic equations by completing the square and using the quadratic formula.
Solve equations that are reducible to quadratic equations.
Find the vertex, the line of symmetry, and the maxima or minima of the graph of a quadratic function using the method of completing the square.
Graphquadratic functions.
2.3 POLYNOMIAL MODELS AND CURVE FITTING
Solve applications using polynomial models. vFit quadratic, cubic, and quartic polynomial functions to data and make predictions.
2.4 POLYNOMIAL DIVISION; THE REMAINDER AND FACTOR THEOREMS
Do long division with polynomials and determine whether one polynomial is a factor of another.
Use synthetic division to divide a polynomial by x-c.
Use the remainder theorem to find a function value f(c).
Use the factor theorem to determine whether x-c is a factor of f(x).
2.5 THEOREMS ABOUT ZEROS OP POLYNOMIAL FUNCTIONS
Factor polynomial functions and find the zeros and their multiplicities.
Findapolynomial withspecifiedzeros.
For a polynomial function with integer coefficients, find the rational zeros and the other zeros, if possible.
For a polynomial function with rational coefficients, find the rational zeros and the other zeros, if possible.
2.6 RATIONALFUNCTIONS
Graph a rational function, identifying all asymptotes.Solve applications involving rational functions.
2.7 POLYNOMIAL AND RATIONAL INEQUALITIES
Solve polynomial and rational inequalities.
TEST
CHAPTER 3 EXPONENTIAL AND LOGARJTHMIC FUNCTIONS
3.1 INVERSE FUNCTIONS
Determine whether a function is one-to-one, and if it is, find a formula for its inverse.
Simplify expressions of the type (f · f')(x) and (fl · f)(x).
3.2 EXPONENTIAL FUNCTIONS AND GRAPHS
Graph exponential equations and functions.
Solve problems involving applications of exponential functions and their graphs.
3.3 LOGARITHMIC FUNCTIONSAND GRAPHS
Graphlogarithmic functions.
Convertbetweenexponential andlogarithmicequations.
Find common and natural logarithms on a grapher.
3.4 PROPERTIES OFLOGARITHMIC FUNCTIONS
Convert from logarithms of products, powers, and quotients to expressions in terms of individual logarithms, and conversely.
Simplify expressions of the type log------
3.5 SOLVING EXPONENTIAL AND LOGARITHMIC EQUATIONS
Solve exponential and logarithmic equations.
3.6 APPLICATIONS AND MODELS: GROWTH AND DECAY
Solve applications involving exponential growth and decay.
Find models involving exponential and logarithmic functions.
TEST
CHAPTER 4 SYSTEMS AND MATRICES
4.1 SYSTEMS OFEQUATIONS IN TWOVARIABLES
Solve a system of two liIlear equations in two variables by graphing.
Solve a system of two linear equations in two variables using the substitution and the elimination methods.
Use systems of two linear equations to solve applied problems.
4.2 SYSTEMS OF EQUATIONS IN THREE OR MORE VARIABLES
Solve systems of linear equations in three or more variables.
Use systems of three equations to solve applied problems.
Model a situation using a quadratic function.
4.3 MATRICES AND SYSTEMS OFEQUATIONS
Solve systems of equations using matrices.
4.4 MATRIX OPERATIONS
Add, subtract, and multiply matrices when possible.
Write a matrix equation equivalent to a system of equations.
4.5 INVERSES OFMATRICES
Find the inverse of a square matrix, if it exists.
Use inverses of matrices to solve systems of equations.
4.6 SYSTEMS OFINEQUALITIES AND LINEARPROGRAMMING
Graph linearinequalities.
Graph systems of linear inequalities. · Solve linear programming problems.
4.7 PARTIAL FRACTIONS
Decompose rational expressions into partial fractions.
TEST
CHAPTER 6 SEQUENCES, SERIES, AND COMBINATORICS
6.1 SEQUENCESAND SERIES
Find terms of sequences given the nth term.
Look for a pattern in a sequence and try to determine a general term.
Convert between sigma notation and other notation for a series.
Given a recursively defined sequence, construct terms.
6.2 ARITHMETIC SEQUENCES AND SERIES
For any arithmetic sequence, find the nth term when n is given and n when the nth term is given, and given two terms, find the common difference and construct the sequence.
Find the sum of the first n terms of an arithmetic sequence.
Insert arithmetic means between two numbers.
6.3 GEOMETRIC SEQUENCES AND SERIES
Identify the common ratio of a geometric sequence, and find a given term and the sum of the first n terms.
Find the sum of an infinite geometric series, if it exists.
6.4 MATHEMATICAL INDUCTION
List the statements of an infinite sequence that is defined by a formula.
Do proofs by mathematical induction.
6.5 COMBINATORICS: PERMUTATIONS
Evaluate factorial and permutation notation and solve related applications.
6.6 COMBINATORICS: COMBINATIONS
Evaluate combination notation and solve related applications.
6.7 THE BINOMIAL THEOREM
Expand a power ofa binomial using Pascal's triangle or factorial notation.
Find a specific term of a binomial expansion.
Find the total number of subsets of a set of n objects.
6.8 PROBABILITY
Compute the probability of a simple event.
Go to PAGES 2 - 6. SKILLS TEST
Go to PAGES 7 - 11. OBJECTIVES
Go to PAGES 12 - 13. ASSIGNMENTS
Go to PAGES 14 - 15. SUGGESTIONS ON HOW TO STUDY MATHEMATICS
Go to PAGE 15. HAVING TROUBLE WITH MATHEMATICS?
Go to PAGE 16. MATHEMATICS DEPARTMENT POLICIES
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William V. Thayer,
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