Solutions to Activity 1

Investigation:

1. All real numbers
2. 0 and 1
3. x>= -1

A bit further:

1. When x>=-1
2. Answers are the same.

Students should now realize that they now have two ways of solving the equation. The used their prior knowledge of finding the intersection of two points and using the domain to solve the system of inequalities.

Just a bit more:

Method 1:

1. The graphs are the same.

The students should begin to wonder why they have the same graph but with a different equation.

Method 2:

1. (-1,0)
2. When x>=-1
3. The answers are the same.

The students should be able to recognize that the last method of getting one side of the inequality equal to zero uses the same methods as finding the y-intercept when solving equations. This will show various ways of solving the same type of problem. Students can now pick which method they feel most comfortable with.

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