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VERTEX AND SLOPE OF LINEAR GRAPH
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 CartesianPlane

  • Finddistance between two points in the Cartesian Plane.
  • Usethe Distance formula to solve Geometry and real-life applicationproblems.
  • Findthe Midpoint of the segment joining two points in the Cartesian Plane.
  • Usethe Midpoint formula to solve application problem.


 Graphsof Equations

  • Determinewhether a point lies on the graph of an equation.
  • Sketchgraphs using a table of values and a graphing utility.
  • Findthe x and y-intercepts of the graph of an equation(algebraically and graphically).
  • Determinethe symmetry of the graph of an equation (algebraically andgraphically).
  • Writethe General Form Equation of a circle in Standard Form and determinethe center and radius of the circle.

 GraphingUtilities

 Linesin the plane

  • Determinethe slope of a line passing through two points.
  • Findthe point-slope form equation of a line.
  • Findslope-intercept form equation of a line and sketch the line.
  • Determineif lines are parallel or perpendicular using slope.
  • Writeequation of a line parallel or perpendicular to a given line.

LinearModeling

  • Constructlinear models.
  • Uselinear models with slope as the rate of change.
  • Finda linear model that fits a set of data (Linear Regression).

 Functions

  • Determineif an equation or a set of ordered pairs represents a function.
  • Usefunction notation.
  • Evaluatea function.
  • Findthe domain of a function.
  • Interpretinput and output of Real-life functions.
  • Solvean application problem involving Real-life functions.

 Graphsof Functions

  • Find the domain and range using the graph of a function.
  • Vertical Line Test.
  • Describe the increasing and decreasing behavior of afunction.
  • Classify a function as even or odd.
  • Identify six common graphs.

 Transformationsof Functions

  • Describe how a graph has been changed from the originalusing common transformations.
  • Sketch the graph of a function using the common graphs andtransformations.
  • Write the equation of a function using common graphs andtransformations.

 Algebraof Functions

  • Find the sum, difference, product, and quotient of functions
  • Find the composition of two functions
  • Determine the domain of two combined functions
  • Determine the functions which have been composed to make upa given function
  • Solve real life problems involving the combination(addition,subtraction, multiplication, division, and/or composition) of twofunctions

 InverseFunctions

  • Determineif a function has an inverse function (Horizontal Line Test).
  • Findthe Inverse of a function.
  • Grapha function and its Inverse.
  • Restrictingthe Domain to Create a Function with an Inverse Function

QuadraticFunctions

  • Sketchthe graph of a quadratic function (parabola) and identify its vertexand intercepts (algebraically and graphically).
  • Writea quadratic function in standard form and identify the vertex from thestandard form.
  • Findthe quadratic function given the vertex and a point on the graph
  • Solvereal-life problems involving quadratic functions.

PolynomialFunctions of Higher Degree

  • Classifypolynomial functions as constant, linear, quadratic, cubic, etc.
  • Applythe Leading Coefficient Test to determine right and left behavior ofthe graph of a polynomial function
  • Find the real zeros of polynomial by factoring
  • Write the equation of a polynomial given its roots and apoint on the graph.

PolynomialDivision

  • Dividepolynomials using long division.
  • Divise polynomials using syntheticdivision.
  • Use the Remainder Theorem to evaluate a polynomial.
  • Use the Factor Theorem to factor a polynomial.

 

 

RealZeros of Polynomials

  • Findall possible rational zeros of a polynomial function using the RationalZero Test.
  • Findall real zeros of a polynomial function algebraically.
  • Approximatethe real zeros of a polynomial function using the Intermediate ValueTheorem.
  • Approximatethe real zeros of a polynomial using a graphing utility.
  • Write the equation of a polynomial given its roots and apoint on the graph.

ComplexNumbers

  • Add, subtract, multiply, and divide complex numbers.
  • Write a complex number in standard form.
  • Solvea quadratic equation involving complex zeros.

PolynomialFunctions

  • Usethe Fundamental Theorem of Algebra and the Linear Factorization Theoremto write a polynomial as the product of linear factors.
  • Findall real and complex zeros of a polynomial function.
  • Finda polynomial with integer coefficients whose zeros are given.
  • Usethe Leading Coefficient Test and the zeros of a polynomial to sketchthe graph of a polynomial.
  • Applytechniques for approximating real zeros to solve an application problem

RationalFunctions

  • Findthe domain of a rational function.
  • Findthe vertical and horizontal asymptotes of the graph of a rationalfunction.
  • Sketchthe graph of a rational function.
  • Usea rational function model to solve an application problem

ExponentialFunctions

  • Sketchthe graph of an exponential function.
  • Find basic characteristics of an exponential function(domain, range,intercepts, increasing/decreasing behavior).
  • Writeformulas of transformed exponential functions,
  • Usean exponential model to solve an application problem (in particular,models involving the natural exponential function and compound interestformulas).
  • Usethe compound interest formula to solve finance problems.

LogarithmicFunctions

  • Sketchthe graph of a logarithmic function.
  • Investigatebasic characteristics of a logarithmic function (domain, x-intercept,vertical asymptote).
  • Writeformulas of transformed logarithmic functions.

Laws of Logarithms

  • Usethe change of base formula to evaluate a logarithm.
  • Applyproperties of logarithms.


Exponentialand Logarithm Equations

  • SolveLogarithmic and Exponential Equations.


Exponentialand Logarithm Models:

  • Usea logarithmic model to solve an application problem (in particular,models involving the natural logarithmic function).
  • Constructand use a model for exponential growth or exponential decay.

Systemsin Two Variables - Substitution

  • Solvea linear system of equations by the method of substitution.
  • Solvea nonlinear system of equations by the method of substitution.
  • Constructand use a linear system of equations to solve an application problem.
Systemsin Two Variables -Graphing
  • Solvea linear system of equations graphically.
  • Solvea nonlinear system of equations graphically.
  • Constructand use a linear system of equations to solve an application problem.

Systemsin Two Variables -Elimination

  • Solvea linear system of equations by the method of elimination.
  • Constructand use a linear system of equations to solve an application problem.

SigmaNotation and Factorials

  • Evaluatea factorial expression.
  • Usethe summation notation to write the sum of a sequence.

Sequences- Basic Concepts

  • Findthe terms of a sequence.
  • Findthe sum of a finite sequence.
  • Usea sequence to solve an application problem


ArithmeticSequences & Series

  • Determine whether a sequence isarithmetic or geometric.
  • Findthe nth term of an arithmetic sequence.
  • Finda formula for an arithmetic sequence.
  • Findthe sum of a finite arithmetic series.
  • Usean arithmetic sequence to solve an application problem.

GeometricSequences and Series:

  • Determinewhether a sequence is arithmetic or geometric.
  • Findthe nth term of a geometric sequence.
  • Finda formula for a geometric sequence.
  • Findthe sum of a finite geometric series.
  • Find the sum of an infinite geometric series (wherepossible).
  • Usea geometric sequence to solve an application problem.