Invite students to share their answers and reasons. The goal of the discussion is for students to consider some reasons why we might want the operation of taking the square root to give us only one number. Here are some questions for discussion if needed:

• “The solutions to the equation are approximately 1.414 and -1.414. If represents only one of the exact solutions, which of the approximations would you choose? How could you write the other exact solution?” (I would choose the positive number because looks positive to me. The other solution could be written .)
• “Suppose represents both solutions to . Now suppose that Clare is solving this equation because it represents a square with an area of 2 square units and she wants to find the side length of the square. How could she show that she wants only the positive solution?” (She could write out the phrase “the positive part of .”)
• “Do you think it makes sense to choose the meaning of ? That is, would it make sense to let that symbol sometimes mean only the positive number and sometimes mean both numbers?” (That would get very confusing. I think it makes sense to choose one of the meanings and stick with it.)
• “Would you rather the symbol represent only one of the solutions to or both solutions?” (I would rather it represent only the positive solution.)
• Tell students that mathematicians use the convention that , or , represents only the positive solution to . This convention helps in being precise about what is meant.

The purpose of this discussion is to emphasize that the rule is a function. Invite students to share their reasoning about why it is a function. Then ask students,

• “Why is it important that the rule is a function when you want to use the graph of to find the value of ? (Because it is a function, there is only one value on the graph above or below 5 on the -axis.)
• “Describe what a graph of the equation looks like.” (It would look like , but also have another part in which the shape is reflected over the -axis. It looks like a parabola opening to the right.)

Display the graph of .

Then ask students, “How can you tell that the graph of is not a function?” (For some inputs it has more than one output. For example, the points and are both on the graph.)