Math 102

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Outline

Chapter Outline

Chapter-by-chapter outline:

• Chapter 1: Equations and Inequalities
• Chapter 2: Graphs
• Chapter 3: Functions and their Graphs
• Chapter 4: Linear and Quadratic Functions
• Chapter 5: Polynomial and Rational Functions
• Chapter 6: Exponential/Log Functions
• Chapter 8: Systems of Equations and Inequalities

Section Outline

Chapter 1: Equations and Inequalities

• Linear equations
• Quadratic equations
• Radical equations and factorable equations
• Solving inequalities
• Equations and inequalities with absolute value
• Applications (interest, rate, mixture)

Chapter 2: Graphs

• Distance/Midpoint formulas
• Graphs of equations in 2 variables
• Lines

Chapter 3: Functions and their Graphs

• Functions
• Graphs of functions
• Properties of functions
• Library of functions, piecewise functions
• Graphing transformations
• Building functions (modeling)

Chapter 4: Linear and Quadratic Functions

• Linear functions and properties
• Linear models and functions from data
• Quadratic functions and properties
• Quadratic models and functions from data and descriptions
• Inequalities with quadratics

Chapter 5: Polynomial and Rational Functions

• Polynomial functions and models
• Properties of rational functions
• Graphs of rational functions
• Polynomial and rational inequalities
• Real zeros of polynomials

Chapter 6: Exponential/Log Functions

• Composition functions
• One to one functions and inverse functions
• Exponential functions
• Logarithmic functions
• Properties of logs

*Log and exponential equations

• Financial models

*Exponential growth and decay

• Logistic growth and decay
• Building log/exp models

Chapter 8: Systems of Equations and Inequalities

• Systems of linear equations: substitution, elimination
• Systems of linear equations: matrices
• Systems of linear equations: determinants
• Matrix algebra
• Partial fractions decomposition
• Systems of nonlinear equations
• Systems of inequalities
• Linear programming

Objective Outline

Chapter 1 Objectives

You should be able to do the following...

Section 1.1:

• Solve a linear equation
• Solve equations leading to linear equations
• Solve problems modeled by linear equations

Section 1.2:

• Solve quadratic equation by factoring
• Solve quadratic equation by completing the square
• Solve quadratic equation using quadratic formula
• Solve problems modeled by quadratic equations

Section 1.4:

• Solve radical equations
• Solve equations quadratic in form
• Solve equations by factoring

Section 1.5:

• Use interval notation
• Use properties of inequalities
• Solve inequalities

Section 1.6:

• Solve equations involving absolute value
• Solve inequalities involving absolute value

Section 1.7:

• Translate verbal descriptions into mathematical expressions
• Solve interest problems
• Solve mixture problems
• Solve uniform motion problems

Chapter 2 Objectives

Section 2.1:

• Use the distance formula
• Use the midpoint formula

Section 2.2:

• Graph equations by plotting points
• Find intercepts from a graph
• Find intercepts from an equation
• Test an equation for symmetry with respect to the x-axis, the y-axis, and the origin
• Know how to graph key equations

Section 2.3:

• Calculate and interpret the slope of a line
• Graph lines given a point and a slope
• Find the equation of a vertical line
• Use the point-slope form of a line
• Write equation of a line given two points, identify horizontal lines
• Write equation of a line in slope-intercept form
• Identify slope and y-intercept of line from its equation
• Graph lines written in general form using intercepts
• Find equations of parallel lines
• Write equations of perpendicular lines

Chapter 3 Objectives

Section 3.1:

• Determine whether a relation represents a function
• Find the value of a function
• Find the domain of a function defined by an equation
• Form the sum, difference, product, and quotient of two functions

Section 3.2:

• IDentify the grpah of a function
• Obtain information from or about the graph of a fucntion

Section 3.3

• Determine even and odd functions from a graph
• Dientify even and odd functions from the equation

*Guse a graph to dtermine whetre a funcitno is inc dec or constant

• * Use graph to locate local min max
• USE grpah to locate abs min miax
• Use graphing utility to locate approx local min max
• Find average rate of change of function

Section 3.4:

• Graph functions listed in library of functions
• Graph piecewise defined functions
• Graph functions using vertical and horizontal shifts
• Graph functions using compressions and stretches
• Graph functions using reflection about x-axis or y-axis
• Build and analyze functions

Chapter 4 Objectives

Section 4.1:

• Graph linear functions
• Use average rate of change to identify linear functions
• Determine whether linea rr function is incr decr or const
• build linear models from verbal descr

Section 4.2:

• Draw nad interpret scatter diagrams
• Distinguish between linear and nonlinera relations
• Use graping utility to find line of best fit

Section 4.3:

• Graph a quadratic function using transformations
• Identify the vertex and axis of symmetry of quad func
• Grpah quad func using vertex, axis, and intercepts
• Find quad function given its vertex and one other point
• Find the max or min value of a quad func

Section 4.4:

• Build quadratic models from verbal descriptions
• Build quadratic models from data

Section 4.5:

• Solve inequalities involving a quadratic function

Chapter 5 Objectives

Section 5.1:

• Identify polynomial functions and their degree
• Graph polynomial functions using transformations
• Identify the real zeros of a polynomial function and their multiplicity
• Analyze the graph of a polynomial function
• Build cubic models from data

Section 5.2:

• Find the domain of a rational function
• Find the vertical asymptotes of a rational function
• Find the horizontal or oblique asymptote of a rational function

Section 5.3:

• Analyze the graph of a rational function
• Solve applied prob.ems involving rational functions

Section 5.4:

• Solve polynomial inequalities
• Solve rational inequalities

Section 5.5:

• Use the remainder and factor theorems
• Use the rational zeros theorem to list the potential rational zeros of a polynomial function
• Find the real zeros of a polynomial funciton
• Solve opoynoial equations
• Use the Theorem for Bounds on Zeros
• Use intermediate value theorem

Section 5.6:

• Use the conjugate pairs theorem
• Find a polynomial function with specified zeros
• Find the complex zeros of a polynomial

Chapter 6 Objectives

Section 6.1:

• Form a composite function
• Form the domain of a composite function

Section 6.2:

• Determine whether a function is one-to-one
• Determine the inverse of a ffunction defined yb a map or a set of ordered pairs
• Obtain the graph of the inverse funciton from the graph of the funcitno
• Find the inverse of a funciton defined by an equation

Section 6.3

• Evaluate exponential functions
• Grha exp functions
• Define e

8 Solve exponential equations

Section 6.4

• Change exp statements to log statements and log statements to exp statements
• Evaluate log expressions
• Determine domain of log function
• Graph log functions
• Solve log equations

Section 6.5:

• Work with the properties of logs
• Write a log expression as a sum or difference of logs
• Write a log expression as a single log
• Evaluate logs whose base is neither 10 nor e

Section 6.6:

• Solve log equations
• Solve exponential equations
• Solve log and exponential equations using a graphing utility

Section 6.7:

• Determine the future value of a lump sum of money
• Calculate effective rates of return
• Determine the present value of a lump sum of money
• Determine the rate of interest or time required to double a lump sum of money

Section 6.8:

• Find equations of populations obeying law of uninhibited growth
• Find equations of populations obeying law of decay
• Use Newton's Law of Cooling
• Use logistic models

Section 6.9:

• Build exp model from data
• Build log model from data
• build logistic model from data

Chapter 8 Objectives

Section 8.1:

• Solve systems of equations by substitution
• Solve systems of equations by elimination
• Identify inconsistent/impossible linear systems
• Express solution of system of dependent equations containing two variables
• Solve systems of three equations containing three variables
• Identify incosnistent ssytems of equations with 3 variables
• Express solution of system of dependent equations containing three variables

Section 8.2:

• Write augmented matrix of system of linear equations
• Write the system of equations from augmented matrix
• Perform row operations on matrix
• Solve system of linear equations using matrix

Section 8.3

• Evaluate 2x2 determinant
• Use Cramer's rule to solve system of equations with two vars
• Evaluate 3x3 determinant
• Use Cramer's rule to solve a 3x3 system
• Know the properties of determinants

Section 8.4

• Find sum and diff of two matrices
• Find scalar multiples of a matrix
• Find product of 2 matrices
• Find inverse of a matrix
• Solve system of linear equations using an inverse matrix