Gizmos for Idaho - Mathematics: Functions (Content Standards adopted 2022)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

F.IF: : Interpreting Functions

F.IF.A: : Understand the concept of a function and use function notation.

F.IF.A.1: : Demonstrate understanding that a function is a correspondence from one set (called the domain) to another set (called the range) that 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.3: : Demonstrate that a sequence is a function, sometimes defined recursively, whose domain is a subset of the integers.

F.IF.B: : Interpret functions that arise in applications in terms of the context. Include linear, quadratic, exponential, rational, polynomial, square root and cube root, trigonometric, and logarithmic functions.

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 maxima and minima; 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: : Analyze functions using different representations.

F.IF.C.7: : Graph functions expressed symbolically and show key features of the graphs, by hand in simple cases and using technology for more complicated cases.

F.IF.C.7.a: : Graph linear and quadratic functions and show intercepts, maxima, and minima.

F.IF.C.7.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F.IF.C.7.c: : Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

F.IF.C.7.d: : Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

F.IF.C.7.e: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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.a: : Use the process of factoring and/or completing the square in quadratic and polynomial functions, where appropriate, to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F.IF.C.8.b: : Use the properties of exponents to interpret expressions for exponential functions. Apply to financial situations such as identifying appreciation and depreciation rate for the value of a house or car sometime after its initial purchase.

F.IF.C.10: : Given algebraic, numeric and/or graphical representations of functions, recognize the function as polynomial, rational, logarithmic, exponential, or trigonometric.

F.BF: : Building Functions

F.BF.A: : Build a function that models a relationship between two quantities.

F.BF.A.1: : Write a function that describes a relationship between two quantities. Functions could include linear, exponential, quadratic, simple rational, radical, logarithmic, and trigonometric.

F.BF.A.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

F.BF.A.1.b: : Combine standard function types using arithmetic operations.

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: : Build new functions from existing functions.

F.BF.B.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Include, linear, quadratic, exponential, absolute value, simple rational and radical, logarithmic, and trigonometric functions. Utilize technology to experiment with cases and illustrate an explanation of the effects on the graph. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F.BF.B.4: : Find inverse functions algebraically and graphically.

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.5: : Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

F.LE: : Linear, Quadratic, and Exponential Models

F.LE.A: : Construct and compare linear, quadratic, and exponential models and solve problems.

F.LE.A.1: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

F.LE.A.1.a: : Demonstrate that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

F.LE.A.1.b: : Identify situations in which one quantity changes at a constant rate per unit interval relative to another.

F.LE.A.1.c: : Identify situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

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 (including reading these from a table).

F.LE.A.3: : Use graphs and tables to demonstrate 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.B: : Interpret expressions for functions in terms of the situation they model.

F.LE.B.5: : Interpret the parameters in a linear or exponential function (of the form f(x) = b^x + k) in terms of a context.

F.TF: : Trigonometric Functions

F.TF.A: : Extend the domain of trigonometric functions using the unit circle.

F.TF.A.1: : Demonstrate radian measure as the ratio of the arc length subtended by a central angle to the length of the radius of the unit circle.

F.TF.A.1.a: : Use radian measure to solve problems.

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 pi/3, pi/4, and pi/6, and use the unit circle to express the values of sine, cosine, and tangent for pi - x, pi + x, and 2pi - 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: : Model periodic phenomena with trigonometric functions.

F.TF.B.5: : Model periodic phenomena using trigonometric functions with specified amplitude, frequency, and midline.

F.TF.C: : Prove and apply trigonometric identities.

F.TF.C.8: : Relate the Pythagorean Theorem to the unit circle to discover the Pythagorean identity sin^2(theta) + cos^2(theta) = 1 and use the Pythagorean identity to find the value of a trigonometric function (sin(theta), cos(theta), or tan(theta)) given one trigonometric function (sin(theta), cos(theta), or tan(theta)) and the quadrant of the angle.

F.TF.C.9: : Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.

Correlation last revised: 2/25/2022

Idaho - Mathematics: Functions

Content Standards | Adopted: 2022

F.IF: : Interpreting Functions

F.BF: : Building Functions

F.LE: : Linear, Quadratic, and Exponential Models

F.TF: : Trigonometric Functions