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College Algebra: Topics to Master

Chapter 1

1.1 ― Rectangular Coordinates
1) Finding the distance between two points.
2) Finding the coordinates of the midpoint of a segment.
3) Drawing scattergraphs.

1.2 ― Graphs of Equations
1) Opening a window to see the complete graph of an equation.
2) Finding the x- and y- intercepts of an equation .

1.3, 1.5 ― Solving Equations
1) Solving equations analytically:
a) linear (with and without fractions)
b) quadratic by:
i. factoring
ii. square root property
ii. quadratic formula
c) rational (check for extraneous solutions )
d) radical
i. cube root
ii. square root (check for extraneous solututions)
e) absolute value (check for extraneous solutions)

2) Solving formulas.

3) Solving equations graphically :
a) x- intercept method
b) intersection of graphs method

1.4 ― Applications: Word problems modeling linear and quadratic equations.

1.6 ― Solving Inequalities
1) linear
2) combined
3) absolute value (both <  and >  inequalities)

1.7 ― Lines
1) Finding the equation of the line going through a point and having a given slope
2) Finding the equation of the line given the slope and the y-intercept.
3) Finding the equation of the line going through two points.
4) Finding the equation of the line going through a point and being
parallel/perpendicular to another line.
5) Finding the slope and y-intercept from an equation in the general form.
6) Word problems modeling the equation of the line.
a) Break Even Analysis
b) Supply and Demand

Chapter 2

2.1 ― Functions
1) Determining whether a relation represents a function.
2) Determining whether a graph is that of a function.
3) Evaluating functions at:
a) numbers
b) expressions
4) Finding the domain, range, symmetry and intercepts from a graph.
5) Finding the domain of a function analytically:
a) for polynomial functions
b) for fractional functions .
c) for square root functions
d) for a mix of (b) and (c)
6) Word problems

2.2 ― Linear Functions and Models
1) Straight Line Depreciation
2) Drawing a scattergraph, finding the line of best fit with the calculator , and using the equation
to predict.

2.3 ― Quadratic Functions
1) Quadratic functions:
a) finding the vertex analytically.
b) finding the intercepts
c) graphing by hand.
d) finding the range.
2) Word problems modeling quadratic functions.

2.4 ― Quadratic Functions and Models
1) Word problems modeling optimizations of quadratic functions.

Chapter 3

3.1 - 3.3 ― Properties of Functions, Library of Functions
1) Telling whether a graph is symmetric with respect to the x-axis, y-axis or neither.
2) Mastering elementary functions:
a) constant
b) linear
c) square
d) cube
e) square root
f) reciprocal
g) absolute value
h) greatest integer
3) Using a graph to determine
a) domain
b) range
c) intervals of increase, decrease, or constant
d) even, odd, or neither
e) intercepts
4) Evaluating and graphing piece-wise defined functions.
5) Determining whether a function defined by an equation is even, odd, or neither.
6) Word problems modeling optimization of functions.

3.4 ― Graphing Techniques: Transformations
1) vertical shift
2) horizontal shift
3) vertical stretch
4) vertical compression
5) reflection about the x-axis
6) reflection about the y-axis

3.5 ― Operations on functions
1) Operations with functions:
a) addition /subtraction (and domain)
b) multiplication/division (and domain)
c) composition (and domain)
2) De-composition of functions.
3) Word problems modeling composition.

3.6 ― Applications
1) Word problems: constructing functions

Chapter 4

4.1 ― Power functions
1) Graphing transformations of power functions y = x^n (with n odd, or even)
2) Word problems modeling power functions

4.2 ― Polynomial functions
1) Recognizing polynomial functions
2) Writing the equation of a polynomial function of a given degree and given
3) Determining the end behavior of a polynomial function.
4) Determining the number of turning points
5) Graphing polynomial functions and determining:
a) x-intercepts (for some functions do this analytically)
b) y-intercept
c) multiplicity of zeros
d) local extrema points
6) Solving polynomial equations
7) Cubic regression

4.3-4.4 ― Rational functions
1) Determining
a) domain
b) vertical asymptote
c) horizontal asymptote
d) intercepts
e) graphing
2) Word problems modeling rational functions

4.5 ― Polynomial and Rational Inequalities
1) Solving polynomial inequalities analytically
2) Solving rational inequalities analytically
3) Word problems modeling polynomial functions

Chapter 6

6.1 ― One to one functions. Inverse functions
1) Given a function defined by an arrow graph determine whether the inverse is a
2) Given the graph of a function, determine whether it is one to one.
3) Given the graph of a function, graph its inverse
4) Given two functions, verify they are inverses by showing that the composition = x.
5) Given a function, find its inverse.

6.2 ― Exponential Functions
1) Graphing transformations of exponential functions
2) Word problems modeling exponential functions

6.3 ― Logarithmic Functions
1) Changing an exponential expression to an equivalent logarithmic expression
2) Changing a logarithmic expression to an equivalent exponential expression
3) Evaluating logarithms with and without the calculator
4) Finding the domain of logarithmic functions
5) Graphing transformations of logarithmic functions
6) Word problems modeling logarithmic functions

6.4 ― Properties of Logarithms
1) Expanding by writing as a sum or difference of logarithms
2) Condensing by writing as a single logarithmic expression
3) Evaluating logarithms with the change of base formula
4) Graphing logarithmic functions with the calculator

6.5 ― Logarithmic and Exponential Equations
1) Solving logarithmic equations
2) Solving exponential equations

6.6 ―Compound Interest
Word problems involving:
a) simple interest
b) compound interest
c) compounding continuously
d) present value

6.7― Growth and Decay
Word problems modeling
a) growth
b) decay
c) Newton's law of cooling
d) logistic models

6.8 ― Exponential, Logarithmic, and Logistic curve fitting
Finding the function that best fits the data:
a) exponential
b) logarithmic
c) logistic

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