Getting Started 
Misconception/Error The student does not understand how to graph a step function. 
Examples of Student Work at this Level The student provides a graph that is unrelated to the algebraic description of the function.
The student confuses the use of open and closed dots.

Questions Eliciting Thinking What is a step function?
Can you explain how you graphed this function?
What part of the equation prompted you to graph this?
How would you graph f(x) = 4? 
Instructional Implications Guide the student through each part of the function definition explaining its meaning and sketching its graph. Explain the convention of graphing endpoints of open intervals as open dots and endpoints of closed intervals as closed dots. Remind the student that this convention was used when graphing intervals on a number line.
Review the distinction between the domain and the range of a function. Guide the student to use the graph to identify the domain and range. Encourage the student to use both inequalities and interval notation to describe the domain and range. Provide additional instruction on interval notation if needed.
Provide additional examples of functions defined piecewise for the student to graph. Include examples given in context, such as parking fees at an airport that are given as hourly rates that vary depending on the number of hours parked [see MFAS task Airport Parking (FIF.2.5)] or cost per item of large tshirt orders that vary based on quantities ordered. Ask the student to graph each example and describe its domain and range. 
Moving Forward 
Misconception/Error The student is unable to correctly represent the domain or the intercept of the function. 
Examples of Student Work at this Level The student graphs the step function correctly. However, the student makes errors in describing the domain or the intercepts of the function. The student:
 Describes the range instead of the domain and describes the intercept incorrectly.
 Describes the domain as a continuous interval from 4 to 4 and may make errors with regard to the inclusion of the endpoints of this interval.

Questions Eliciting Thinking What is the domain of a function? What is the range?
What is happening to the graph in the interval 1 < x < 2? Is this interval part of the domain? 
Instructional Implications Review the distinction between the domain and the range of a function. Provide instruction on determining the domain and range of a function from its graph. Provide several additional examples of graphs of functions and ask the student to find the domain and range of each. Encourage the student to use both inequalities and interval notation to describe the domain and range. Provide additional instruction on interval notation if needed. 
Almost There 
Misconception/Error The student makes a minor error when defining the domain of the function. 
Examples of Student Work at this Level The student correctly graphs the function and identifies the yintercept as (0, 1) but when describing the domain, the student:
 Uses an incorrect inequality symbol, describing the domain as Â and 2 < x < 4.
 Omits a negative sign, describing the domain asÂ Â and .
 Uses interval notation but uses a bracket in place of a parenthesis or vice versa.
 Uses interval notation but uses the â€śintersectâ€ť symbol instead of the â€śunionâ€ť symbol, , or completely omits the symbol.

Questions Eliciting Thinking There is a minor error with the way you described the domain. Can you find and correct it?
What is the difference between these two symbols:Â and ? How are these symbols read and what do they mean? 
Instructional Implications Provide feedback to the student concerning any errors that were made and allow the student to revise his or her work. Review, as needed, the use of interval notation. Be sure the student understands the distinction between the symbolsÂ Â andÂ .
Provide additional opportunities to represent domains and ranges of functions using inequalities and interval notation.
Consider implementing other MFAS graphing tasks such as Graphing a Linear Function (FIF.3.7) and Graphing a Quadratic Function (FIF.3.7). 
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 correctly graphs the step function and describes the domain usingÂ inequalities,Â Â and , or usingÂ interval notation, [4, 1) [2, 4). 
Questions Eliciting Thinking Can you write the domain in interval notation?
What is the range of this function? 
Instructional Implications Challenge the student to graph a more complex step or piecewise function which includes linear and quadratic functions.
Consider implementing other MFAS graphing tasks such as Graphing Root Functions (FIF.3.7), Graphing a Rational Function (FIF.3.7), and Graphing an Exponential FunctionÂ (FIF.3.7). 