Students will learn to identify the domain and endpoint of the graph of a radical function by examining the equation.

Looking back over a number of examples, students make use of the structure of equations to anticipate the graph.

2 minutes

As students enter the room, I tell them to pick up where they left off with yesterday’s assignment (Graphing Radical Functions Day 1). If they were required to complete any of the graphs at home, I instruct them to begin by comparing their graphs with those of their peers. In the best case, all of the students will have the same, correct graphs. If not, then I would expect some conversations to start among the students as they attempt to figure out whose graphs are correct – if any.

30 minutes

15 minutes

In the wrap-up conversation at the end of this lesson I find it’s important to draw several points out of the students by asking simple questions. Typically, I would write a new equation on the board, similar to those on the worksheet, and ask for help making a graph.

- “Where/how do I begin my graph?” The students may interpret this two ways: I may be asking for the endpoint of the graph, or I may be asking generally how to begin graphing a function. The conversation should include:
- “select values for
*x*, and then compute corresponding*y*-values” - “examine the radicand to predetermine the domain”
- “remember that the square root of x^2 is the
*absolute value*of*x*” - “the endpoint will be (
*a, b*) if*f*(*x*) =*b*+ sqrt(*x*-*a*)”

- “How do a solve for
*f*(*x*) = 5?” The students should instruct me to graph the horizontal line*y*= 5 and to estimate the intersection point. - “What if I had asked to solve for
*x*= 5?” The students should respond with something like “That’s easy! Just evaluate*f*(5),” but I would also help them to see the solution graphically with the vertical line*x*= 5. - If time permits, I would initiate a conversation about the graphs of various power functions and their corresponding radical functions. This should lead to the observation that there are two general behaviors depending on the parity of the power/root.

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