IA1.AT.D: Model with functions.

Model with functions.

IA1.AT.D.13Analyze and model arithmetic and geometric sequences using recursive and explicit representations. a. Identify whether a sequence is arithmetic or geometric and create an explicit rule to describe the pattern. b. Rewrite a recursive representation of an arithmetic or geometric sequence to an explicit rule. c. Model contexts involving arithmetic or geometric patterns using an explicit or recursive rule, and use the rule to solve problems.IA1.AT.D.14Represent functions using tables and graphs, and interpret key features in context. Key features include: domain, intercepts, intervals of increase and decrease, positive and negative values, end behavior, asymptote, and points of transition between pieces. a. Analyze linear and exponential functions by identifying patterns in tables and graphs. Distinguish between constant and proportional growth. b. Extend the understanding of functions to include piecewise-defined and absolute value functions. Represent them in tables and graphs and explain how absolute value functions can be represented as a specific case of piecewise functions. c. Relate key features of a function’s graph and table to the characteristics of a context, and justify the appropriateness of a function model based on that context.IA1.AT.D.15Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Given a relationship in context where the rate of change over equal intervals is constant, identify it as linear and create a linear function to model the relationship. b. Given a relationship in context where a quantity changes by a constant percent per unit interval relative to another, identify it as exponential and create an exponential function to model the relationship.IA1.AT.D.16Analyze how changes to a function’s input or output affect the graph and its meaning in context. a. Identify how replacing f(x) with f(x + k) and f(x) + k changes the graph of a linear, exponential, or absolute value function. Describe the direction of the change and determine the value of k when given a graph. b. Explain how changing the input or output of a function affects the quantities represented in context. Use the structure and features of the parent function to justify how these changes impact the initial context.IA1.AT.D.17Find and interpret the inverse of a linear function in context. a. Show that a linear function is one-to-one and therefore has an inverse that is also a function. b. Find the inverse of a linear function represented with an equation or a table. c. Interpret the meaning of the inverse in context as a relationship that maps outputs of the original function back to their corresponding inputs.

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