Section	Teacher-facing learning goals
Functions and Their Representations	Lesson 1 Interpret descriptions and graphs of functions in context. Understand that a relationship between two quantities is a function if there is only one possible output for each input. Use words and graphs to represent relationships that are functions, including identifying the independent and dependent variables. Lesson 2 Interpret statements that use function notation and explain (orally and in writing) their meaning in terms of a situation. Understand that function notation is a succinct way to name a function and specify its input and output. Use function notation to express functions with specific inputs and outputs. Lesson 3 Describe connections between statements that use function notation and a graph of the function. Practice interpreting statements that use function notation and explaining (orally and in writing) their meaning in terms of a situation. Sketch a graph of a function given statements in function notation. Lesson 4 Create tables and graphs to represent a function given statements in function notation. Interpret rules of functions that are expressed using function notation. Use function notation to write equations that represent rules of functions. Lesson 5 Evaluate functions and solve equations given in function notation, either by graphing or by reasoning algebraically. Understand linear function as a function whose output changes at a constant rate and whose graph is a line. Use technology to graph and evaluate functions given in function notation.
Analyzing and Creating Graphs of Functions	Lesson 6 Analyze connections between statements that use function notation and features of graphs and describe (orally and in writing) these connections. Interpret key features of a graph—the intercepts, maximums, minimums, and the intervals when the function is increasing or decreasing—in terms of a situation. Understand and be able to use the terms “horizontal intercept,” “vertical intercept,” “maximum,” and “minimum” when talking about graphs of functions. Lesson 7 Given a graph of a function, estimate or calculate the average rate of change over a specified interval. Recognize that the slope of a line joining two points on a graph of a function is the average rate of change. Understand that the average rate of change describes how fast the output of a function changes for every unit of change in the input. Lesson 8 Given a verbal or visual representation of a situation, sketch a graph and show key features. Interpret the average rate of change in a situation. Practice interpreting key features of graphs and explaining (orally and in writing) their meaning in terms of a situation. Lesson 9 Compare key features of graphs of functions and interpret them in context. Interpret equations of the form \( f(x)=g(x)\) in context and recognize that the solutions to such an equation are the \(x\)-coordinates of the points where the graphs of \(f\) and \(g\) intersect. Interpret statements about two or more functions written in function notation.
A Closer Look at Inputs and Outputs	Lesson 10 Given a description of a function that represents a situation, determine reasonable domain and range. Understand that the domain of a function is the set of all possible inputs and the range is the set of all possible outputs. Lesson 11 Given a description of a function that represents a situation, determine reasonable domain and range. Practice interpreting key features of graphs in terms of the quantities represented. Lesson 12 Interpret a graph of a piecewise function or the rules given in function notation, and explain the rules (orally and in writing) in terms of a situation. Sketch a graph that represents the rules of a piecewise function, paying special attention to the endpoints of each interval. Understand a piecewise function as a function defined by different rules for different intervals of the domain. Lesson 13 Analyze and describe (orally and in writing) features of a scatter plot that relates guesses and absolute errors. Generalize (using words or equations) the relationship between guesses and absolute errors. Given a set of numerical guesses and a target number, calculate absolute errors and create a scatter plot of the data. Lesson 14 Analyze and describe (orally and in writing) the effects of adding a constant term to an expression defining an absolute value function. Define absolute value function in terms of the distance of the input from 0. Interpret an absolute value function described in words or in function notation, and create a table of values and a graph to represent the function.
Inverse Functions	Lesson 15 Given a linear function in context, describe (using words or equations) its inverse function. Recognize that if one function takes \(a\) as its input and gives \(b\) as its output, its inverse function takes \(b\) as its input and gives \(a\) as the output. Understand that the inverse of a linear function can be found by reversing the process that defines the initial function. Lesson 16 Find the inverse of a linear function by solving an equation for the input variable. Interpret an inverse function in terms of the quantities in a situation. Lesson 17 Find the inverse of a linear function given in function notation. Write a linear function and an inverse function to model data and solve problems.
Putting it All Together	Lesson 18 Use functions to model real-life situations and make predictions.

Alg1.4: Functions