| A | B | C | D | E | |
|---|---|---|---|---|---|
1 | Understands and applies the characteristics of a function. | ||||
2 | Click on links to see FULL Guidance | Oregon Math Standards & Guidance | Highly Proficient | Proficient | Nearing Proficient |
3 | HS.AFN.A.1 | Understand a function as a rule that assigns a unique output for every input and that functions model situations where one quantity determines another. | Provides examples and nonexamples of functions using a variety of mathematical and authentic contexts. Nuanced descriptions demonstrate clearly all the components of a function relationship and how they are met or not in a given relation. Explains why function relationships are important in mathematics and in authentic contexts. | Identifies functions presented in different representations (graph, table, equation, context). Explains how the definition of a function is or is not satisfied by a given representation. Correctly defines a function relationship and provides examples of function and non function relationships. For example: explains why it is important that there is a 1-to-1 relationship between user name and password but not necessarily between password and username for a popular website or app. | Correctly names input and output in a function relationship. Describes rules that connect inputs with outputs. Given a graph correctly identifies functions using a vertical line test. |
4 | HS.AFN.A.2 | Use function notation and interpret statements that use function notation in terms of the context and the relationship it describes. | Uses correct function notation in a variety of contexts with precision. Example: Explains how function notation is used to define recursive functions. Explains the meaning of f(n) and f(n-1) notation. | Interprets and uses function notation with tables graphs and equations. For example: writes a function C which maps a temperature in Fahrenheit to its corresponding value in Celsius. C(f) = 9/5 * (f - 32). For example: Expresses that for example, in an imagined scenario the height of a tree can be represented as a function of time which means that given any point in time we can compute an estimate for the height of the tree. | Given the definition of a function like: f(x) = ⅔ * x + 5 correctly computes function values. Converts between equation forms like y = 3x + 1 and function notation, recognizing that y = f(x). |
5 | HS.AFN.B.4 | Compare properties of two functions using multiple representations. Distinguish functions as members of the same family using common attributes. | Uses the structure of an expression and the properties of operations (exponentiation, multiplication/division, addition/subtraction) to explain important properties of different functions. | Compares key characteristics of exponential functions with the key characteristics of linear and exponential functions. Observe using graphs and tables that a quantity is increasing. For example: Given a graph of one function and an algebraic expression for another, determine which has the larger y-intercept. Given a graph of one function and an algebraic equation for another, students should be able to determine which has the larger y-intercept. | Recognizes concrete properties of a function in given representations. For example: recognizes the x- and y- intercepts on a graph, or slope of a line written in slope-intercept form y = mx + b. Compare key characteristics of functions when given the same representation (i.e. two graphs) |
6 | HS.AFN.B.5 | Relate the domain of a function to its graph and to its context. | Writes the domain and range of continuous and discrete functions using correct set and interval notation Determine appropriate domain restrictions for problems in a new or unfamiliar context. | Writes the domain and range of continuous and discrete functions using correct set and interval notation in familiar contexts. Determine appropriate domain restrictions for problems in familiar contexts. | Determines appropriate domain restrictions in familiar contexts For example: If the function h(n) gives the number of hours it takes a person to assemble n engines in a factory, then the set of positive integers would be an appropriate domain for the function. |
7 | HS.AFN.C.6 | Interpret key features of functions, from multiple representations, and conversely predict features of functions from knowledge of context. | Interprets key characteristics of linear functions in context using correct set and interval notation. | Identifies, predicts and writes key features of function presented in any representation from a context with mathematically precise notation. | Describes key features of a function presented without manipulating the representation (identifies intervals of increase on a graph, identifies the maximum value in a table) |
8 | HS.AFN.C.7 | Graph functions using technology to show key features. | Graphs functions expressed symbolically or with tables Graphs key features (specific values, domain/range, discrete/continuous, intercepts; intervals of increasing/decreasing, positive/negative; relative maxima/minima) Reason about how changes to the viewing window or scale will affect or not affect different characteristics of the graph. | Graphs linear and exponential functions by hand or by using technology. Estimates the rate of change given a graph and including different scales and units on each axis. | Uses technology to graph a function and find the value of key features. Estimates the rate of change given a graph and including the same scales of the axis. |
9 | HS.AFN.D.8 | Model situations involving arithmetic patterns. Use a variety of representations such as pictures, graphs, or an explicit formula to describe the pattern. | Makes connections between linear functions and arithmetic sequences presented in contextual situations. Builds and interprets arithmetic sequences as functions presented graphically and algebraically. Add, and subtract linear functions and explain how the properties of the resulting function are determined by this process. | Builds an explicit function (linear or exponential) to describe or model a relationship between two quantities. Adds, and subtracts linear functions and describe the properties of the resulting function. | Continues a pattern to find a missing term in an arithmetic sequence. Finds the common difference from a table of values or arithmetic sequence. Write recursive rules for arithmetic sequences in informal ways (next = previous + 2, first = 5) |
10 | HS.AFN.D.10 | Explain why a situation can be modeled with a linear function, an exponential function, or neither. In a given model, explain the meaning of coefficients and features of functions used, such as slope for a linear model. | When given contextual problems explains why a situation can be modeled with a linear function, exponential function or neither. Explains the meaning of the coefficients, constants and features of function in the context | Uses the content learned in this course to create a mathematical model to explain real-life phenomena. For example: Modeling the amount of savings using linear or exponential models (depending on assumptions) | Identifies situations in which one quantity changes at a constant rate per unit interval relative to another. Identifies situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. |