Maryland: Functions Math Standards

47 standards · 4 domains

BUILDING FUNCTIONS

F.BF.A.1 Write a function that describes a relationship between two quantities.
F.BF.A.1.a Determine an explicit expression, a recursive process, or steps for calculation from a context.
F.BF.A.1.c Compose functions.
F.BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
F.BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and 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.
F.BF.B.4 Find inverse functions.
F.BF.B.4.b Verify by composition that one function is the inverse of another.
F.BF.B.4.c Read values of an inverse function from a graph or a table, given that the function has an inverse.
F.BF.B.4.d Produce an invertible function from a non-invertible function by restricting the domain.
F.BF.B.4.e Build inverse trigonometric functions.
F.BF.B.5 Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

INTERPRETING FUNCTIONS

F.IF.A.1 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.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F.IF.A.2.a Extend evaluating functions to include operations with composite functions, e.g. f(x + 2) - f(x).
F.IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
F.IF.B.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal 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.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F.IF.B.6 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.
F.IF.C.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.C.7.f Graph all functions including piecewise-defined functions, step functions and absolute value functions
F.IF.C.7.g Determine the end behavior of the graph of a polynomial function using the degree and leading coefficient.
F.IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F.IF.C.8.c Interpret the behavior of the graph of a function using the concept of limits.
F.IF.C.8.d Estimate limits algebraically, numerically and graphically.
F.IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
F.IF.C.10 Describe the behavior of a sequence.

LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

F.LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.
F.LE.A.1.d Distinguish between situations that can be modeled with exponential functions and logistic functions.
F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F.LE.A.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
F.LE.A.4 For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.
F.LE.A.4.a Use properties of logarithms, including both common and natural logarithms, to rewrite and solve exponential models.
F.LE.B.5 Interpret the parameters in a linear or exponential function in terms of a context.
F.LE.B.5.a Interpret the parameters in a logistic function in terms of a context.
F.LE.B.6 Build and interpret logistic functions to model real-world problems.
F.LE.B.6.a Sketch and analyze the graphs of logistic functions.
F.LE.B.6.b Compare and contrast the exponential, logarithmic, and logistic models.
F.LE.B.6.c Apply understanding of logarithmic and logistic functions to solve real-world problems.

TRIGONOMETRIC FUNCTIONS

F.TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.
F.TF.A.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.A.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 x, π + x, and 2π – x in terms of their values for x, where x is any real number.
F.TF.A.4 Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.
F.TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.
F.TF.B.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.B.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.C.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 of the angle.
F.TF.C.9.a Use trigonometric identities to rewrite expressions and as a tool when solving trigonometric equations.