Getting Started 
Misconception/Error The student does not understand the concept of domain. 
Examples of Student Work at this Level Instead of describing the domain, the student:
 Writes a linear equation that models the graphed points,Â y = 5x  20.
 Attempts to describe the slope of the line containing the graphed points.
 Mistakes the domain for the xintercept (or yintercept).
 Makes an observation about the functional relationship.

Questions Eliciting Thinking What do you know about the term domain? Is the domain of a function the same as the slope? Is the domain the xintercept?
Which values in a function make up the domain? How can you identify them on a graph?
Which values in a function make up the range? How can you identify them on a graph? 
Instructional Implications Describe the domain of a function as the set of all input values or xcoordinates for which the function is defined. Model finding an appropriate domain for a function from its graph by identifying and describing the xcoordinates of all points on the graph. Guide the student to identify a number system (e.g., integers or real numbers) that describes the kinds of numbers in the domain as well as the specific domain elements. Provide the student with the graphs of a variety of functions and ask the student to describe both their domains and ranges. If necessary, review the meaning of open and closed circles on graphs and their significance in describing the domain. Remind the student to identify the domain and range not only from a graph, but to consider the context of the function when one is given. Provide the student with additional opportunities to describe the domain of a function from its graph.
Provide instruction on ways to describe sets of numbers (e.g., using inequalities, setbuilder notation, and interval notation). Emphasize that when describing the domain of a function, one must consider the number system from which the domain is drawn as well as the specific elements in the domain. Provide a verbal description of a number set [e.g., the set of real numbers from 4 to 17 (inclusive)] and ask the student to use both set builder notation and interval notation to represent the set. 
Making Progress 
Misconception/Error The student does not completely and accurately describe the domain. 
Examples of Student Work at this Level The studentâ€™s response indicates an understanding of the concept of domain but includes errors in its description.
The student:
 Verbally describes the domain but is not specific about the values it includes.
 Describes the domain as increasing by one each time.
 Verbally describes the domain as the xaxis, the number of cars washed, and a total of 12 cars.

Questions Eliciting Thinking Can you describe the domain in words? What values are in the domain? Does the domain contain any rational values such as 123.7?
What kinds of numbers are included in the domain? What are their specific values?
How is a set of numbers typically described in mathematics? What do you know about roster, setbuilder, and interval notation?
What inequality could be used to describe the domain? 
Instructional Implications Explain the difference between discrete and continuous sets and provide examples of each. Guide the student to consider both the graph of the function (whether it is continuous or consists of discrete points) and the independent variable (e.g., number of cars washed) when deciding from which number system the domain is drawn. Provide instruction on ways to describe sets of numbers (e.g., using inequalities, setbuilder notation, and interval notation). Emphasize that when describing the domain of a function, one must consider the number system from which the domain is drawn as well as the specific elements in the domain. Provide a verbal description of a number set [e.g., the set of integers from 2 to 9 (inclusive)] and ask the student to use both set builder notation and the roster method to represent the set.
Provide the student with additional opportunities to describe the domain of a function from its graph. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student describes the domain of the graphed function using the roster method, {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} or using setbuilder notation, . 
Questions Eliciting Thinking Is the domain a discrete or continuous set?
What are the intercepts for this function? What do they mean in the context of the graph?
How many cars do they need to wash to make a profit? Can the club make a profit of $3.00? Why or why not? 
Instructional Implications If not done so already, introduce the student to a variety of ways to describe sets of numbers such as roster, setbuilder, and interval notation.
Ask the student to describe the range of the graphed function using appropriate notation.
Ask the student to model the graph with an equation. Then ask the student to use the equation to determine the profit when 20 cars are washed and the number of cars that need to be washed to make a profit of $215. 