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Kansas: Functions Math Standards

45 standards · 4 domains

BUILDING FUNCTIONS

F.BF.1 Use functions to model real-world relationships.
F.BF.1a (9/10) Combine multiple functions to model complex relationships. For example, p(x) = r(x) - c(x); (profit = revenue - cost).
F.BF.1b (11) Determine an explicit expression, a recursive function, or steps for calculation from a context.
F.BF.1c (11) Compose functions. For example, if T(y) is the temperature in the atmosphere as a function of height, and h(t) is the height of a weather balloon as a function of time, then T(h(t)) is the temperature at the location of the weather balloon as a function of time.
F.BF.2 (+) Write arithmetic and geometric sequences and series both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
F.BF.3 (9/10/11) Transform parent functions (f(x)) by replacing f(x) with f(x) + k, kf(x), f(kx), adn f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. For (9/10) focus on linear, quadratic, and absolute value functions.
F.BF.4 Find inverse functions.
F.BF.4a (11) Write an expression for the inverse of a function.
F.BF.4b (11) Read values of an inverse function from a graph or a table, given that the function has an inverse.
F.BF.4c (+) Verify by composition that one function is the inverse of another.
F.BF.4d (+) Produce an invertible function from a non-invertible function by restricting the domain.
F.BF.5 (11) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

INTERPRETING FUNCTIONS

F.IF.1 (all) Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
F.IF.2 (all) Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.IF.3 (9/10/11) Recognize patterns in order to write functions whose domain is a subset of the integers. (9/10) Limited to linear and quadratic. For example, find the function given {(−1,4),(0,7),(1,10),(2,13)}.
F.IF.4 (all) For a function that models a relationship between two quantities, interpret key features of expressions, graphs and tables in terms of the quantities, and sketch graphs showing key features given a description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
F.IF.5 (all) Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
F.IF.6 (9/10/11) Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. (9/10) limited to linear functions.
F.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F.IF.7a (9/10) Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.
F.IF.7b (11) Graph square root, cube root, and exponential functions.
F.IF.7c (11) Graph logarithmic functions, emphasizing the inverse relationship with exponentials and showing intercepts and end behavior.
F.IF.7d (+) Graph piecewise-defined functions, including step functions.
F.IF.7e (11) Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
F.IF.7f (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
F.IF.7g (+) Graph trigonometric functions, showing period, midline, and amplitude.
F.IF.8 Write a function in different but equivalent forms to reveal and explain different properties of the function.
F.IF.8a (9/10) Use different forms of linear functions, such as slope-intercept, standard, and point-slope form to show rate of change and intercepts.
F.IF.8b (11) Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
F.IF.8c (11) Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^t, y = (0.97)^t, y = 91.01)^12t, y = (1.2)^(t/10), and classify them as representing exponential growth or decay.
F.IF.9 (all) Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, a quantity increasing exponentially eventually exceeds a quantity increasing linearly.

LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

F.LQE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
F.LQE.1a (11) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
F.LQE.1b (11) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
F.LQE.1c (11) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
F.LQE.2 (11) Construct exponential functions, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

TRIGONOMETRIC FUNCTIONS

F.TF.1 (+) Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
F.TF.2 (+) Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.
F.TF.3 (+) Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4, and π/6, and use the unit circle to express the values of sine, cosine, and tangent for π-x, π+x, and 2π - x in terms of their values for x, where x is any real number.
F.TF.4 (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
F.TF.5 (+) Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
F.TF.6 (+) Understand that restricting a trigonometric function to a domain on which it is always increasing or always decreasing allows its inverse to be constructed.
F.TF.7 (+) Use inverse functions to solve trigonometric equations that arise in modeling contexts; evaluate the solutions using technology, and interpret them in terms of the context.
F.TF.8 (+) Prove the Pythagorean identity sin^2(ϴ) + cos^2(ϴ) = 1 and use it to find sin(ϴ), cos(ϴ), or tan(ϴ) given sin(ϴ), cos(ϴ), or tan(ϴ) and the quadrant.
F.TF.9 (+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.