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Define a logarithm and use logarithmic properties
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Order
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Description
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1
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Define a logarithm
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2
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Use logarithmic properties to determine values of logarithmic expressions
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3
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Solve logarithmic and exponential equations using properties of logarithms
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Define and graph a logarithmic function; find domain and range; and solve applications
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Order
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Description
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1
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Define a logarithmic function
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2
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Determine the domain and range of logarithmic functions
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3
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Draw the graph of logarithmic functions
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4
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Solve applications involving logarithmic functions
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Define, determine domain and range, and graph the six circular functions
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Order
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Description
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1
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Define the six circular functions
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2
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Describe the domain and range of the six circular functions
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3
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Draw the graph of circular functions using amplitude, period, and phase shift
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Define the six trigonometric functions; use to solve right/oblique triangles and solve applications
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Order
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Description
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1
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Define six trigonometric functions
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2
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Solve right triangles using trigonometric functions
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3
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Solve applications involving right triangles using the trigonometric functions
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4
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Solve oblique triangles using the law of sines and law of cosines
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Use trigonometric identities to prove other identities and work with the inverse trig. functions
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Order
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Description
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1
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Use the fundamental trigonometric identities to prove other identities
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2
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Use the sum and difference identities to prove other identities
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3
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Use the double angle and half-angle identities to prove other identities
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4
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Determine the domain and range of the trigonometric functions and their inverses
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5
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Draw the graph of the trigonometric functions and their inverses
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Define and work with vectors
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Order
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Description
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1
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Define vectors
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2
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Find the components of a vector
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3
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Perform operations on vectors
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4
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Solve application problems involving vectors
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Define and work with complex numbers
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Order
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Description
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1
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Define a complex number
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2
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Describe complex numbers in standard, rectangular, polar, and trigonometric forms
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3
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Draw the graph of a complex number on the Argand diagram
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4
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Perform operations on complex numbers
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5
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Use DeMoivre's Theorem to find powers and roots of complex numbers
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Define basic concepts related to functions and their graphs
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Order
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Description
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1
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Define Function
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2
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Define domain and range of function
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3
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Define maximum and minimum values of a function
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4
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Define increasing, decreasing, and constant functions
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5
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Define end behavior of a function
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6
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Define zeros and roots of a function
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7
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Define transformation of a function
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Graph a function using a graphing calculator
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Order
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Description
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1
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Draw the graph of a function using a graphing calculator
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Define and graph linear functions and solve applications involving them
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Order
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Description
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1
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Define a linear function
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2
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Draw the graph of a linear function
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3
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Solve applications that involve linear functions
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Define and graph quadratic functions and solve applications involving them
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Order
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Description
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1
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Define a quadratic function
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2
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Draw the graph of a quadratic function
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3
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Determine the vertex and the maximum or minimum value of a quadratic function
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4
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Solve applications involving quadratic functions
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Perform operations involving functions including finding the inverse of a function
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Order
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Description
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1
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Determine the sum of two functions
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2
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Determine the difference of two functions
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3
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Determine the product of two functions
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4
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Determine the quotient of two functions
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5
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Determine the composition of two functions
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6
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Compute a the value of a composition of two functions given a domain value
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7
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Determine the inverse of a function
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Define and graph polynomial functions including end behavior and zeros (real and imaginary)
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Order
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Description
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1
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Define polynomial functions
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2
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Draw the graph of a polynomial function
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3
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Determine the end behavior of a polynomial function using the leading term test
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4
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Determine all the real and imaginary zeros of a polynomial function
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5
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Draw the graph of transformations of polynomial functions
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Define and graph rational functions including basic characteristics and transformations
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Order
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Description
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1
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Define a rational function
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2
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Determine the domain and range of a rational function
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3
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Determine the vertical and horizontal asymptotes of a rational function
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4
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Draw the graph of a rational function
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5
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Draw the graph of a transformation of a rational function
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Define, evaluate, and graph exponential functions and use them to model phenomena
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Order
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Description
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1
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Define an exponential function
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2
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Calculate the value of an exponential function
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3
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Determine the domain and range of an exponential function
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4
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Draw the graph of an exponential function
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5
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Draw the graph of transformations of exponential functions
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6
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Use exponential functions to model natural phenomena such as exponential growth and decay and practical situations such as compound interest
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