Clare was adding and , and at first she wrote . But then she remembered that 2 and -2 both square to make 4, and that 3 and -3 both square to make 9.

She wrote down all the possible combinations:

    2 + 3 = 5
    2 + (-3) = -1
    (-2) + 3 = 1
    (-2) + (-3) = -5

Then she wondered, “Which of these are the same as ? All of them? Or only some? Or just one?”

How would you answer Clare’s question? Give reasons that support your answer.

1. Complete the table.

   	0	1	4	9	16	25	36

2. Use the values from the table to plot seven points on the graph of . Then sketch the graph by smoothly connecting the points you drew.

   

3. Is the rule a function? Explain your reasoning.

4. Explain how you could use the graph to find any solutions to the equation . How many solutions are there?

5. Use the graph to approximate the value of . Explain your reasoning.

6. Approximate any solutions to the equation . Explain your reasoning.