Getting Started 
Misconception/Error The student does not demonstrate an understanding of absolute value functions and their graphs. 
Examples of Student Work at this Level The student:
 Does not attempt to write the equations.
 Rewrites the given equation for each graph.
 Writes one or two linear equations for each graph.

Questions Eliciting Thinking What type of graphs are these?
What do you know about absolute value equations? What is the standard form of an absolute value equation?
How are these graphs different from the graph of y = x?
How are the differences in the graphs represented in their equations? 
Instructional Implications Review the basic form of an absolute value function. Provide the student with absolute value functions of the form y = x + b and y = x + c to graph (using technology or by hand) and compare to the graph of y = x. Assist the student in observing the relationship between the constants and the direction and magnitude of the shift. Next, provide absolute value functions of the form y = mx. Again, guide the student to observe the effect that m has on the slope of the graphs.
Allow the student to further explore absolute value functions using a graphing calculator or an interactive site such as Math Is Fun (http://www.mathsisfun.com/data/functiongrapher.php). Have the student predict the effect of changing the parameters of an absolute value function on its graph and then check the prediction using a graphing calculator or an interactive website.
If not used previously, consider using MFAS task Comparing Functions â€“ Absolute Value (FBF.2.3). 
Moving Forward 
Misconception/Error The student has an incomplete understanding of absolute value functions and their graphs. 
Examples of Student Work at this Level The student makes one or more of the following errors:
 Represents a horizontal translation as a vertical translation (or vice versa).
 Represents a horizontal translation to the left as a horizontal translation to the right.
 Uses the wrong coefficient of x to describe the graph of y = 3x.

Questions Eliciting Thinking Did you check any of your equations by graphing or by making a table of values?
What kind of values of x will causeÂ y = x + 3 to be different thanÂ y =x + 3? What is the value of each expression when x = 5? How do you suppose their graphs compare?
How are the differences in the graphs represented in their equations? 
Instructional Implications Encourage the student to make a table of values for the equations he or she wrote and then compare those values to points on the graphs.
Review with the student the standard form of an absolute value equation, y = amx + b + c. Remind the student that the value of b will shift the graph left (if b is positive) or right (if b is negative) while the value of c shifts the graph up (if c is positive) or down (if c is negative). Ask the student to reevaluate the equations he or she originally wrote.
Allow the student to further explore absolute value functions using a graphing calculator or an interactive site such as Math Is Fun (http://www.mathsisfun.com/data/functiongrapher.php). Have the student predict the effect of changing the parameters of an absolute value function on its graph and then check the prediction using a graphing calculator or an interactive website.
If not used previously, consider using MFAS task Comparing Functions â€“ Absolute Value (FBF.2.3). 
Almost There 
Misconception/Error The student does not understand the effect on the equation of changing the slope of the graph of an absolute value function. 
Examples of Student Work at this Level The student correctly writes the equations of graphs that are horizontal or vertical translations of y = x. However, the student is unable to write the equation of the third graph. For this graph, the student may:
 Not attempt to write an equation.
 Write an incorrect equation such as y = x and explain this is the equation because â€śthe graph did not shift.â€ť
 Write the equation as if a horizontal or vertical shift occurred (e.g., y = x + 3 or y = x â€“ 3).

Questions Eliciting Thinking How does the third graph compare to the graph of y = mx? How are these graphs alike? How are they different?
How would the graph of y = 3x compare to the graph of y = x? How are these graphs alike? How are they different? 
Instructional Implications Review with the student the standard form of an absolute value equation, y = amx + b + c. Relate the effect of m on the graph of an absolute value function to the effect of m on the graph of a linear function.
Allow the student to further explore absolute value functions using a graphing calculator or an interactive site such as Math Is Fun (http://www.mathsisfun.com/data/functiongrapher.php). Â Have the student predict the effect of changing the parameters of an absolute value function on its graph and then check the prediction using a graphing calculator or an interactive website. 
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 writes the following equations:
 y = x + 3
 y = x + 2
 y = 3x or y = 3x

Questions Eliciting Thinking Is there another equation you could have written for the third graph?
Can you explain why 3x = 3x?
What would make the graph of an absolute value equation open downward? 
Instructional Implications Challenge the student to write equations of graphs the have been translated both vertically and horizontally or that have been translated and have a slope different from 1 and 1.
Have the student explore the effect of a on the graph of y = amx + b + c.
Introduce the student to vertex form of an absolute value equation y = ax  h + k and explain that (h, k) is the vertex of the graph. Encourage the student to interpret vertical and horizontal translations in terms of their effect on the location of the vertex of the graph. 