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    237675

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    Unit 1 — Functions (FN)

    • FN1 — Determine if a relation, equation, or graph defines a function using the definition as well as the vertical line test.
    • FN2 — Use and interpret function notation to evaluate a function for a given input value and find a corresponding input value given an output value.
    • FN3 — Use the graph of a function to find the domain and range in interval notation, the x- and y-intercepts, the maxima and minima, and where it is increasing and decreasing using interval notation.
    • FN4 — Apply transformations including horizontal and vertical shifts, stretches, and reflections to a function. Express the result of these transformations graphically and algebraically.
    • FN5 — Find the sum, difference, product, quotient, and composition of two or more functions and evaluate them.
    • FN6 — Find the inverse of a one-to-one function.

    Unit 1 — Linear Functions (LF)

    • LF1 — Determine the average rate of change of a given function over a given interval. Find the slope of a line.
    • LF2 — Determine an equation for a line when given two points on the line and when given the slope and one point on the line. Express these equations in slope-intercept or point-slope form and determine the slope and y-intercept of a line given an equation.
    • LF3 — Graph a line given its equation or some combination of characteristics, such as points on the graph, a table of values, the slope, or the intercepts.
    • LF5 — Build linear models from verbal descriptions, and use the models to establish conclusions, including by contextualizing the meaning of slope and intercept parameters.

    Unit 1 — Polynomial and Rational Functions (PR1–PR2, quadratics)

    • PR1 — Graph quadratic functions and identify their axis of symmetry, and maximum or minimum point.
    • PR2 — Use quadratic models to solve an application problem and establish conclusions.

    Unit 2 — Trigonometric Functions (TR)

    • TR1 — Convert between degrees and radians. Draw angles in standard position.
    • TR2 — Identify and find coterminal angles. Find the length of a circular arc.
    • TR3 — Use a right triangle to evaluate trigonometric functions.
    • TR4 — Find exact values of trigonometric functions of special angles (30°, 45°, and 60°).
    • TR5 — Use reference angles, signs, and definitions to determine exact values of trigonometric functions.

    Unit 2 — Periodic Functions (PF)

    • PF1 — Determine the basic properties of the graphs of sine and cosine, including amplitude, period, and phase shift.
    • PF2 — Graph trigonometric functions including tangent, cotangent, secant, and cosecant functions and transformations of these functions, and determine the domain and range.
    • PF3 — Determine the inverse sine, cosine, and tangent values; graph inverse trig functions and determine the limitations on the domain and range.

    Unit 3 — Exponential and Logarithmic Functions (EL)

    • EL1 — Determine if a given function is exponential. Find an equation of an exponential function. Evaluate exponential functions (including base e).
    • EL2 — Graph exponential functions and determine the domain, range, and asymptotes.
    • EL3 — Convert between exponential and logarithmic form. Evaluate a logarithmic function, including common and natural logarithms.
    • EL4 — Graph logarithmic functions and determine the domain, range, and asymptotes.
    • EL5 — Use properties of logarithms to condense or expand logarithmic expressions.
    • EL6 — Solve exponential and logarithmic equations.

    Unit 4 — Trigonometric Equations (TE)

    • TE1 — Use the sum and difference, the double-angle, and power-reducing formulas for cosine, sine, and tangent and the Pythagorean identities.
    • TE2 — Symbolically verify identities by using various trig identities.
    • TE3 — Find all solutions to a trigonometric equation.
    • TE4 — Use trigonometric functions and the Pythagorean Theorem to solve right triangles.
    • TE5 — Use the law of sines and/or the law of cosines to solve non-right triangles.
    • TE6 — Solve applications that require the use of trigonometry to find a side or angle.

    Unit 5 — Polynomial and Rational Functions (PR3–PR9)

    • PR3 — Determine the zeros and their multiplicities of a polynomial in factored form. Describe and graph the behavior of a polynomial function at the intercepts and the ends.
    • PR4 — Rewrite a rational function as a polynomial plus a proper rational function (polynomial long division).
    • PR5 — Determine the zeros of a polynomial function with real coefficients.
    • PR6 — Solve rational equations.
    • PR7 — Find the domain and range, vertical and horizontal asymptotes, and intercepts of a rational function and use this information to sketch the graph.
    • PR8 — Solve quadratic inequalities and express the solution graphically and with interval notation.
    • PR9 — Solve rational inequalities and express the solution graphically and using interval notation.