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:
 Attempts to describe the slope of the graphed line.
 Attempts to describe the domain in terms of an ordered pair.
 Attempts to describe the range.

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 a point?
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:
 Does not identify the domain but provides a verbal description in context.
 Describes the scale values shown on the xaxis associated with the domain.
 Lists several discrete values of the domain.
 Describes the domain as {114 â€“ 139} and {153 â€“ 185} or {114, 139} and {153, 185}.

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?
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., height) 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 real numbers from 4 to 17 (inclusive)] and ask the student to use both set builder notation and interval notation 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 indicates that the domain of the first graph is the set of real numbers from 114 cm to 139 cm, inclusive. These values represent the heights of patients between 6 and 13 years old. The domain of the second graph is the set of real numbers from 153 cm to 185 cm, inclusive. These values represent the heights of patients between 14 and 19 years old.
The student may describe the domains using:
 Set builder notation as {: 114 = x = 139} and {: 153 = x = 185}.
 Interval notation as [114, 139] and [153, 185].Â

Questions Eliciting Thinking Is the domain a discrete or continuous set?
Why are there no intercepts?
What kinds of functions are these? 
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 graphs with equations. Then ask the student to use the equations to determine the shoe size of a 6 â€“ 13 year old whose height is 132.5 cm and the height of a 14 â€“ 19 year old whose shoe size is 9. 