Getting Started 
Misconception/Error The student does not understand how to apply the definition of a function to transformations. 
Examples of Student Work at this Level The student does not apply the definition of a function to the transformations.

Questions Eliciting Thinking What is a function? How are functions defined?
How would you apply the definition of a function to a transformation?
What would have to be true of the image of a point in order for a transformation to be a function? 
Instructional Implications Review the definition of a function. Explain that a function is a relation in which each element of the domain is paired with exactly one element of the range or a rule that assigns to each element in the domain a single element of the range. Use the “function machine” analogy to help the student visualize that a function is like a machine that takes a value as an input and transforms it into an output value. Implicit in the “function machine” analogy is the defining property of functions (e.g., that each element of the domain is paired with exactly one element of the range since each input is transformed into a single output). Emphasize that the domain is the set of all “inputs” and the range is the set of all “outputs.”
Consider implementing the MFAS task Identifying Functions (FIF.1.1).
If needed, review the definitions of translations, reflections, rotations, and dilations.
Assist the student in applying the definition of a function to points in the plane. Explain that a transformation is a function if it takes one point in the plane (the input) and transforms it into another point in the plane (the output). Be sure the student understands that the input is a point that can be described by an ordered pair rather than a single value of x. Provide an example of a translation, reflection, rotation, or dilation described algebraically, such as and ask the student to consider whether the transformation maps each input point onto one output point. Model using function notation and the concept of a function to explain and describe transformations. 
Making Progress 
Misconception/Error The student does not understand one or more of the transformations. 
Examples of Student Work at this Level The student understands that a transformation is a function if it maps a point to exactly one image point. However, the student determines that one or more of the transformations is not a function because of a misconception about the transformation. For example, the student says one of the transformations can reflect points to multiple locations.

Questions Eliciting Thinking Can you show me how this transformation maps a point to more than one image point? 
Instructional Implications Ask the student to transform a given point such as (2, 1) according to each transformation and consider if the transformation could actually map this point to more than one image point. Then guide the student to describe each transformation algebraically [e.g., ] and consider if the transformation could map any point to more than one image point.
Provide specific examples of transformations [e.g., or ] and ask the student to determine if each transformation is a function. Ask the student to determine if dilations are functions. 
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 an understanding of each transformation and identifies each as a function. The student explains that each transformation is an example of a function since it maps each point in the plane (the inputs) onto a single point in the plane (the output). The student may rewrite each transformation algebraically [e.g., ] and reason algebraically about the transformation by considering if it is possible for the preimage of a point to be paired with more than one image point.

Questions Eliciting Thinking Are all translations, reflections, and rotations functions?
Are dilations functions? 
Instructional Implications Review function notation and how it can be applied to describing transformations. Model using function notation when describing transformations.
If not done already, ask the student to describe each transformation algebraically [e.g., as and ]. 