In spite of the single reasoning error and the apparent reliance on the table of values in creating the graphs, the student shows proficiency with the requirements of standard HSF-BF.B.3.
HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.
The student made an understanding/reasoning error in #1 by multiplying the absolute value of the input by 3/2, rather than adding 3/2. This error is not computational since all computations were completed correctly. In spite of this error, the verbal description correctly identifies the transformation as a vertical translation. This might have, but did not, help the student catch the error.
2. Comprehension & Application
SMP.6: Attend to precision.
The student shows precision in the language used in descriptions of the transformations.
The student seems to have a limited understanding of the relationship between the function and the graph. The student relies heavily on creating a table of values to guide the student’s graph and descriptions, which demonstrates a point-by-point understanding, rather than a holistic view of transformations.