Students understand set builder notation for the graph of a real-valued function: {(x, f(x)) | x ∈ D}.
Students learn techniques for graphing functions and relate the domain of a function to its graph.

Students understand the meaning of the graph of y = f(x), namely {(x,y) | x ∈ D and y = f(x)}.
Students understand the definitions of when a function is increasing or decreasing.

Students create tables and graphs of functions and interpret key features including intercepts, increasing and decreasing intervals, and positive and negative intervals.

Students use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Students create functions that represent a geometric situation and relate the domain of a function to its graph and to the relationship it describes.

From a graphic representation, students recognize the function type, interpret key features of the graph, and create an equation or table to use as a model of the context for functions addressed in previous modules (i.e., linear, exponential, quadratic, cubic, square root, cube root, absolute value, and other piecewise functions).

Students recognize linear, quadratic, and exponential functions when presented as a data set or sequence, and formulate a model based on the data.

Students create a two-variable equation that models the graph from a context. Function types include linear, quadratic, exponential, square root, cube root, and absolute value. They interpret the graph and function and answer questions related to the model, choosing an appropriate level of precision in reporting their results.

In this Khan Academy activity, students will determine the domain and range of functions from their graph.

This task is designed for students to practice interpreting key features of functions using graphs, a table of values, and situations. The key features of this task include students:
• Applying their knowledge to interpret key features of functions (domain, range, increasing, decreasing, maximum, minimum, intercepts).
• Practicing writing the domain of a function
• Comparing discrete and continuous situations
• Graphing linear and exponential equations and describing key features of the graph

The purpose of this task is to introduce the idea of the domain of a function by linking it to the evaluation of an expression defining the function. By thinking through the evaluation step by step, students isolate the exact point where a given input results in an undefined output.

The purpose of this task is to further define function and to solidify key features of functions given different representations. Features include:

• domain and range
• where the function is increasing or decreasing
• x and y intercepts
• rates of change (informal)
• discrete versus continuous

In this Khan Academy activity, students will determine the domain of a function in a word problem.

Students have been using function notation in various forms and have become more comfortable with features of functions. In this task, the purpose is for students to practice their understanding of the following:
• Distinguish between input and output values when using notation
• Evaluate functions for inputs in their domains
• Determine the solution where the graphs of f(x) and g(x) intersect based on tables of values and by interpreting graphs
• Combine standard function types using arithmetic operations (finding values of f(x)+ g(x))
• Create graphs of functions given conditions.

This task provides opportunities for students to show their understanding of functions in various representations by making matches (3 cards in a set).

Sample Learning Goals
Interpret r (the correlation coefficient) as data points are added, moved, or removed.
Interpret the sum of the squared residuals while manually fitting a line.
Interpret the sum of the squared residuals of a best-fit line as a data point is added, moved, or removed.
Compare the sum of the squared residuals between a manually fitted line and the best-fit line.
Determine if a linear fit is appropriate.

This is a mathematical story to help students in understanding exponential growth.  There are youtube videos of this story that could be used with struggling readers.

The purpose of this task is for students to combine functions, make sense of function notation, and connect multiple representations (context, equations, and graphs). Students will also address features of functions as they solve problems that arise from this context.

The purpose of this task is for students to learn about piecewise functions using their background knowledge of domain, linear functions and function notation. Students will develop an understanding of piecewise-defined functions by

• Using their knowledge of domain to talk about the four ‘pieces’ of the graph that are made up of different linear functions.
• Creating a story for the graph, recognizing how and where the story changes based on each section of the graph.
• Interpreting values for different sections of the graph and identifying which equation from the piecewise function to use based on input/output values.