The student clearly distinguishes between discrete and continuous graphs in the exponential situations, but not in the linear situations.
2. CCSS Alignment
The student distinguishes between situations that can be modeled as linear functions and those that can be modeled as exponential functions.
HSF-LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.
3. CCSS Alignment
The student can construct linear and exponential functions with both explicit and recursive representations. The student does not include the initial value f(0) in the equation, but instead used the term at f(1), and adjusts the equation accordingly.
HSF-LE.A.2: Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
4. Comprehension & Application
SMP.7: Look for and make use of structure.
The student displays very clear structure in each of the explicit and recursive equations, even adjusting the parameters in the explicit equation to reflect the use of the amount present when x = 1. The additional calculations in the work suggest that the student is using the structure of the function type as a tool to facilitate reasoning.