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**1. CCSS Alignment**

The student did not include quantities or direction of transformation in descriptions. The student did not note the location of the reflection (ignored *x*-axis). These would all be expected in a proficient performance for the requirements of HSF-BF.B.3.

**Standard referenced:**

**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.

**2. Understanding**

The student made an error on #4 by confusing vertical compression with a reflection.

**3. Comprehension & Application**

**SMP.6**: Attend to precision.

The student lacked attention to precision of scaling of *y*-axis for graph #4 and does not identify which graphs go with which functions. In addition, the student used prior grade-level vocabulary to describe the vertical translation.

**4. Understanding**

The student used tables on #1-5 as a means of graphing. This makes it unclear whether the student can think about the graph holistically and dynamically, rather than as a discrete collection of ordered pairs.

**5. Understanding**

The student made a computation error by not taking the absolute value in the table. While the graph shows an absolute value graph, the table of values does not coordinate with the graph. In question #4, the student should have been able to identify the calculation error in the table when graphing, but did not.

**1. Understanding**

The student was able to correctly complete the table, describe the transformations, and even plot the discrete points in the table. However, the student was not able to create the graph as required in the prompt.

**1. Understanding**

While the student has correctly provided equations for each of the graphs, the student shows a lack of understanding of the prompt (“write the functions m and n in terms of the function f”) and of how to correctly use the notation.

**2. CCSS Alignment**

The student appears to be able to find the values of k given a graph of a transformation, as required in HSF-BF.B.3.

**Standard referenced:**

**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.