P.5 Factoring Polynomials .
1. Factor basic types of polynomial expressions .
1.1 Graphs and Graphing Utilities
1. Graph the following equation types : linear, quadratic, cubic, radical,
absolute value by plotting points .
2. Demonstrate TI-84+ GRAPHING CALCULATOR SKILLS
4.1 Y=(Enter an equation to be graphed)
4.2 GRAPH (an equation)
4.3 ZOOM (6) ZStandard (Standard Setting)
4.4 WINDOW (change the window settings effectively)
4.5 TABLE (access the Table for an entered equation)
4.6 TBL SET (Set the table appropriately for problem solving)
3. Graph the fol lowing equation types: linear, quadratic, cubic, radical,
absolute value using a graphing utility.
1.5 Quadratic Equations
1. Solve quadratic equations by the square root method.
2. Solve quadratic equations by completing the square.
3. Use the discriminant to determine the kinds of solutions.
4. Solve quadratic equations using the quadratic formula.
5. Determine the most efficient method to use when solving a quadratic equation.
6. Solve application problems that involve a quadratic equation.
7. Solve quadratic equations using the graphing calculator.
8. Answer questions, in writing, about the quadratic equation and how to use it.
1.6 Other Types of Equations
1. Solve polynomial equations by factoring.
2. Solve radical equations.
3. Solve equations with rational exponents.
4. Solve equations that are quadratic in form.
1.7 Linear Inequalities
1. Solve and graph absolute value inequalities.
2. Answer questions, in writing, about absolute value inequalities.
2.1 Introduction to Functions.
1. Determine whether a relation is a function.
2. Determine whether an equation represents a function.
3. Find the domain and range of a relation.
4. Evaluate a function.
5. Graph functions by plotting points.
6. Use the vertical line test to identify functions.
7. Obtain information about a function form its graph.
8. Identify the domain and range of a function from its graph.
9. Identify intercepts from a function ’s graph.
2.2 More on Functions and Their Graphs.
1. Find and simplify a function’s difference quotient .
2. Identify intervals on which a function increases, decreases, or is constant.
3. Determine whether a function is even, odd or neither and recognize their
symmetries.
4. Use graphs to locate relative maxima or minima.
2.5 Transformations of Functions.
1. Recognize graphs of common functions .
2. Use transformations to graph functions.
3. Graph functions involving a sequence of transformations.
3. Use the graph of a function to write a possible equation for the function.
2.6 Combinations of Functions; Composite Functions.
1. Find the domain of a function.
2. Combine functions using the algebra of functions , specifying domains.
3. Form composite functions.
4. Determine domains for composite functions.
5. Write functions as compositions.
2.7 Inverse Functions.
1. Verify inverse functions.
2. Find the inverse of a function and verify that it is the inverse.
3. Use the horizontal line test to determine if a function has an inverse
function.
4. Use the graph of a one-to- one function to graph its inverse function.
5. Find the inverse of a function and graph both function on the same axes with
their line of symmetry.
6. Solve application problems.
2.8 Distance and Midpoint Formulas; Circles.
1. Find the distance between two points.
2. Find the midpoint of a line segment.
3. Write the standard from of a circle’s equation.
4. Give the center and radius of a circle whose equation is in standard form.
5. Convert the general form of a circle’s equation to standard form, give the
center and radius, and graph the circle.
6. Graph a circle centered at the origin using a graphing calculator.
3.1 Quadratic Functions
1. Recognize characteristics of parabolas.
2. Graph parabolas with and without a graphing calculator.
3. Determine a quadratic function’s minimum or maximum value.
4. Solve problems involving minimizing or maximizing quadratic functions.
3.5 Rational Functions and Their Graphs.
1. Find the domain of rational functions.
2. Use arrow notation to describe the behavior of asymptotes.
3. Write the equation of all vertical asymptotes.
4. Write the equation of any horizontal asymptote, after removing holes in the
graph.
5. Graph rational functions and their asymptotes with and without a graphing
calculator.
6. Solve applied problems involving rational functions.
3.7 Modeling Using Variation.
1. Solve direct variation problems.
2. Solve inverse variation problems.
3. Solve combined variation problems.
4. Solve problems involving joint variation.
4.1 Exponential Functions .
1. Evaluate exponential functions.
2. Graph exponential functions.
3. Evaluate functions containing the natural logarithm (base e).
4. Use compound interest formulas.
4.2 Logarithmic Functions.
1. Change from logarithmic to exponential form.
2. Change from exponential to logarithmic form.
3. Evaluate logarithms.
4. Use basic logarithmic properties.
5. Graph logarithmic functions with and without a graphing calculator..
6. Find the domain of a logarithmic function, the intercept, and the equation of
its asymptote.
7. Use inverse properties of logarithms to simplify common and natural log
expressions
4.3 Properties of Logarithms.
1. Use the product rule .
2. Use the quotient rule.
3. Use the power rule.
4. Expand logarithmic expressions.
5. Condense logarithmic expressions.
6. Use the change-of-base property to evaluate logarithmic expressions.
7. Use the change-of-base property and a graphing utility to graph logarithmic
Functions.
4.4 Exponential and Logarithmic Equations.
1. Use like bases to solve exponential equations.
2. Use logarithms to solve exponential equations.
3. Use the definition of a log to solve logarithmic equations.
4. Use the one-to-one property of logarithms to solve logarithmic equations.
5. Solve applied problems involving exponential and logarithmic equations.
4.5 Exponential Growth and Decay; Modeling Data.
1. Model exponential growth and decay.
2. Use logistic growth modeled problems.
3. Model data with exponential and logarithmic functions.
3. Express and solve an exponential model in base e.
5.2 Systems of Linear Equations in Three Variables.
1. Verify the solution of a system of linear equations in three variables.
2. Solve systems of linear equations in three variables.
5.4 Systems of Nonlinear Equations in Two Variables.
1. Recognize systems of nonlinear equations in two variables.
2. Solve nonlinear systems by substitution.
3. Solve nonlinear systems by addition.
4. Solve nonlinear systems by graphing and using the INTERSECT option of the
CALC MENU on the graphing calculator.
5.5 Systems of Inequalities.
1. Graph a linear inequality in two variables.
2. Graph a nonlinear inequality in two variables.
3. Graph a system of inequalities.
4. Graph linear and nonlinear inequalities in two variables on the graphing
calculator. Use the shade option available in front of the function in the Y =
MENU.
