# Functions

## Interpreting Functions (F-IF)

#### Understand the concept of a function and use function notation

CC.9-12.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.

#### Interpret functions that arise in applications in terms of the context

CC.9-12.F.IF.5 – Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

CC.9-12.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.

#### Analyze functions using different representations

CC.9-12.F.IF.7a – Graph linear and quadratic functions and show intercepts, maxima, and minima.

CC.9-12.F.IF.7b – Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

CC.9-12.F.IF.8a – 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.

## Building Functions (F-BF)

#### Build a function that models a relationship between two quantities

CC.9-12.F.BF.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.

## Linear, Quadratic, and Exponential Models (F-LE)

#### Construct and compare linear, quadratic, and exponential models and solve problems

CC.9-12.F.LE.1b – Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

CC.9-12.F.LE.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).

CC.9-12.F.LE.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.

#### Interpret expressions for functions in terms of the situation they model

CC.9-12.F.LE.5 – Interpret the parameters in a linear or exponential function in terms of a context.