DQ 1: Consider the following questions about roots.
What property must a number have to be a “square root of 25 ”? Of what polynomial is it a root? List all the roots of this polynomial (including nonreal roots in C ). Which of these roots should be called the square root of 25 ?
Repeat part (a) for cube roots of 8 .
Repeat part (a) for cube roots of − 8 .
Repeat part (a) for square roots of − 25 .
DQ 2: Let’s Go 4.
Explain how you might introduce the graph of y = 2^x to high school students. With which values of x would you begin? What arguments do you make to fill in the graph?
b) Describe how you would introduce the graph of y = (1/2)^xto high school students.
Compare your ideas with those of your classmates. Were there substantive differences in your approaches to these problems?