### F.IF: Interpreting Functions

#### 1.1: Understand the concept of a function and use function notation.

F.IF.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.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.3: Recognize patterns in order to write functions whose domain is a subset of the integers.

#### 1.2: Interpret functions that arise in applications in terms of the context.

F.IF.4: 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: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F.IF.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.

#### 1.3: Analyze functions using different representations.

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: Graph linear, quadratic and absolute value functions and show intercepts, maxima, minima and end behavior.

F.IF.7b: Graph square root, cube root, and exponential functions.

F.IF.7c: 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: 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: 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: 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.9: Compare properties of two functions using a variety of representations (algebraically, graphically, numerically in tables, or by verbal descriptions).

### F.BF: Building Functions

#### 2.1: Build a function that models a relationship between two quantities.

F.BF.1: Use functions to model real-world relationships.

F.BF.1a: Combine multiple functions to model complex relationships.

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

F.BF.1c: Compose functions.

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.

#### 2.2: Build new functions from existing functions.

F.BF.3: Transform parent functions (f(x)) by replacing f(x) with 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. 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.4: Find inverse functions.

F.BF.4b: 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: Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

### F.LQE: Linear, Quadratic, and Exponential Models

#### 3.1: Construct and compare linear, quadratic, and exponential models and solve problems.

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

F.LQE.1a: 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: Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

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

F.LQE.2: Construct exponential functions, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

### F.TF: Trigonometric Functions

#### 4.1: Extend the domain of trigonometric functions using the unit circle.

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 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.4: Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

#### 4.2: Model periodic phenomena with trigonometric functions.

F.TF.5: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

#### 4.3: Prove and apply trigonometric identities.

F.TF.8: Prove the Pythagorean identity sin²(theta) + cos²(theta) = 1 and use it to find sin(theta), cos(theta), or tan(theta) given sin(theta), cos(theta), or tan(theta) and the quadrant.

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

Correlation last revised: 9/15/2020

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