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COLLEGE ALGEBRA

Chapter 2 FUNCTIONS AND GRAPHS Section: 2.1 – 2.8
Outcomes: The student will review previously learned concepts of graphing on the x-y coordinate plane and analyzing
linear functions , and make real world applications using these skills.
A B C D F N Specific Competencies
Demonstrate the ability to:
2.1 Find the domain and range of a relation.
2.1 Determine whether a relation is a function
2.1 Determine whether an equation represents a function.
2.1 Evaluate a function.
2.1 Graph functions.
2.1 Use the vertical line test to identify functions.
2.1 Obtain information about a function from its graph.
2.1 Identify the domain and range of a function from its graph.
2.1 Identify intercepts from a function’s graph.
*2.2 Find and simplify a function ’s difference quotient .
2.2 Understand and use piecewise functions.
2.2 Identify intervals on which a function increases, decreases, or is constant.
2.2 Use graphs to locate relative maxima or minima.
2.2 Identify even or odd functions and recognize their symmetries.
2.3 Calculate a line’s slope.
2.3 Write the point- slope form of the equation of a line.
2.3 Write and graph the slope-intercept form of the equation of a line.
2.3 Graph horizontal or vertical lines.
2.3 Recognize and use the general form of a line’s equation.
2.3 Use intercepts to graph the general form of a line’s equation.
2.3 Model data with linear functions and make predictions.
2.4 Find slopes and equations of parallel and perpendicular lines.
2.4 Interpret slope as rate of change .
*2.4 Find a function’s average rate of change.
2.5 Recognize graphs of common functions .
2.5 Use vertical shifts to graph functions
2.5 Use horizontal shifts to graph functions.
2.5 Use reflections to graph functions.
2.5 Use vertical stretching and shrinking to graph functions.
2.5 Use horizontal stretching and shrinking to graph functions.
2.5 Graph functions involving a sequence of transformations.
2.6 Find the domain of a function.
2.6 Combine functions using the algebra of functions , specifying domains.
2.6 Form composite functions.
2.6 Determine domains for composite functions.
2.6 Write functions as compositions.
2.7 Verify inverse functions.
2.7 Find the inverse of a function.
2.7 Use the horizontal line test to determine if a function has an inverse function.
2.7 Use the graph of a one-to-one function to graph its inverse function.
2.7 Find the inverse of a function and graph both functions on the same axes.
2.8 Find the distance between two points .
2.8 Find the midpoint of a line segment.
2.8 Write the standard form of a circle’s equation.
2.8 Give the center and radius of a circle whose equation is in standard form.
2.8 Convert the general form of a circle’s equation to standard form.

 

Chapter 3 POLYNOMIAL AND RATIONAL FUNCTIONS Section: 3.1 – 3.7
Outcomes: The student will learn to analyze and graph polynomial functions and solve real-world application
problems involving polynomials.
A B C D F N Specific Competencies
Demonstrate the ability to:
3.1 Recognize characteristics of parabolas including the vertex .
3.1 Graph parabolas.
3.1 Determine a quadratic function ’s minimum or maximum value.
*3.1 Solve problems involving a quadratic function’s minimum or maximum value.
3.2 Identify polynomial functions.
3.2 Recognize characteristics of graphs of polynomial functions.
3.2 Determine end behavior.
3.2 Use factoring to find zeros of polynomial functions.
3.2 Identify zeros and their multiplicities.
*3.2 Use the Intermediate Value Theorem .
*3.2 Understand the relationship between degree and turning points.
3.2 Graph polynomial functions.
3.3 Use long division to divide polynomials.
3.3 Use synthetic division to divide polynomials.
3.3 Evaluate a polynomial using the Remainder Theorem.
3.3 Use the Factor Theorem to solve a polynomial equation.
3.4 Use the rational zero theorem to find possible rational zeros.
3.4 Find zeros of a polynomial function, both real and complex answers (includes
fundamental theorem of algebra).
3.4 Solve polynomial equations.
3.4 Find a polynomial function with given zeros.
*3.4 Use Descartes’s Rule of Signs .
3.5 Find the domain of rational functions.
*3.5 Use arrow notation.
3.5 Identify vertical asymptotes.
3.5 Identify horizontal asymptotes.
3.5 Use transformations to graph rational functions.
3.5 Graph rational functions.
3.5 Identify slant asymptotes.
*3.5 Solve applied problems involving rational functions.
3.6 Solve polynomial inequalities .
3.6 Solve rational inequalities.
*3.6 Solve problems modeled by polynomial or rational inequalities.
3.7 Solve direct variation problems.
3.7 Solve inverse variation problems.
3.7 Solve combined variation problems.
3.7 Solve problems involving joint variation.

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