Students will be able to graph simple radical functions by hand and solve for specified values both graphically and analytically.

Systems of rational and linear equations may be solved graphically by observing the point where the graphs intersect.

5 minutes

This lesson requires very little introduction. The students are already quite familiar with graphing functions, and should be able to do so without too much trouble. If anything, a brief reminder of what it means to solve a system of equations *graphically* may be necessary. Since the solution is only approximate, and based on a picture, most of my students are hesitant to accept it. This will motivate them to also solve the system algebraically. Students are instructed to begin working *individually* and *without* graphing calculators.

10 minutes

For the next ten minutes, I meander throughout the room having brief discussions with individual students about their work. I will help them to identify mistakes, clarify instructions, and confirm what is correct. In particular, a number of them will need help with the cubic parabola and the cube root function. Also, I expect several to initially confuse the *horizontal* line *f*(*x*) = 1 with the *vertical* line *x* = 1. In every case, my aim is to help students to identify their own mistakes simply by asking them pointed questions about their work.

30 minutes