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Analyze the features of a graph of a given function or relation
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
graph a relation or function in x and y
differentiate between symmetry about the x-axis, the y-axis, and the origin
determine the domain and range of a relation or function
define a 1-1 function
apply the horizontal line test for a 1-1 function
determine the inverse function of a 1-1 function
specify the relation between the domain and the range of a function and its inverse
apply basic transformations to the elementary functions
differentiate among elementary functions
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Solve linear and quadratic equations and inequalities
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
relate the solution of an equation to the x-intercept of a graph of the function and to the root (or zero) of the function
solve linear equations and inequalities
use appropriate notations when writing solutions of inequalities
solve quadratic equations using more than one method
use modeling techniques to solve applied problems
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Analyze the properties of linear and quadratic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
graph quadratic functions
apply multiple transformations to quadratic functions
determine the composition of two functions
create new functions by using function operations
note when function composition is non-commutative
apply transformations as compositions of functions
determine the characteristics of a quadratic function
find zeros of quadratic functions algebraically and graphically
convert between standard and graphing form of a quadratic function
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Analyze polynomials
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
find zeros of polynomial functions
determine whether a function is increasing or decreasing on an interval
determine the behavior of a polynomial function at the end points of its domain
use graphical methods to estimate the roots of a polynomial equation
identify local and global extrema
apply the intermediate value theorem
use the fundamental theorem of algebra to determine the number of roots of a polynomial equation
use the fundamental theorem of algebra to determine the number of roots of a polynomial function
identify the degree of a polynomial function
determine all solutions to polynomial equations including complex solutions
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Analyze rational functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
simplify complex fractions
identify removable discontinuities
graph rational functions
perform arithmetic operations with rational expressions
determine the domain of rational functions
determine all asymptotes
solve rational equations
solve rational inequalities (optional)
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Analyze radical functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve radical equations
graph radical functions
verify solutions to identify extraneous roots
determine the domain of radical expressions
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Analyze exponential and logarithmic functions
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
define exponential functions with an arbitrary base
graph an exponential function with an arbitrary base
model exponential functions to real life applications
solve exponential equations
define logarithmic functions with an arbitrary base
identify the inverse relationship between the logarithmic function and the exponential function
graph a logarithmic function with an arbitrary base
solve logarithmic equations
determine the domain and range of logarithmic functions
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Solve algebraic systems
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
solve nonlinear systems of equations
solve systems of linear equations in three or more variables
use systems of three equations to solve applied problems
graph systems of linear inequalities
graph systems of nonlinear equations
solve systems of equations using matrices (optional)
introduce partial fraction decomposition (optional)
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Analyze conic sections
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
identify all conic sections based on a graph
identify all conic sections based on an equation
analyze the characteristics of all conic sections
sketch the graph of all conic sections given their equations
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Analyze series and sequences (optional)
Assessment Strategies
Oral, Written, Graphic and/or Skill Assessment
Criteria
find terms of sequences given the nth term
convert between sigma notation and other notation for a series
find the nth term of an arithmetic and geometric sequence
find the common ratio of a geometric sequence