In mathematics, we are encouraged to look at concepts in three ways: algebraically, graphically, and numerically. From its name, a graphing calculator can be used to look at equations graphically. But newer versions of these calculators can aid us in looking at problems numerically as well through built-in tables, and older versions can also be programmed to generate tables of data. 

Consider a linear equation of the , where y is a function of x. We choose to consider linear equations in this form first because we are guaranteed of one and only one solution. (Can you verify that this is always true? Hint: Draw lines that do not have one solution or only one solution, and determine their equations.) 

If you have a line connecting two points and one point is on one side of the x-axis and the other point is on the other side, what must be true? The line must cross the x-axis at a point somewhere between these two points. 

Find the solution to the equation . Looking at the first table of data, you can see that the solution to this linear equation is somewhere between -2 and -1. By resetting the table values, we can find a closer approximation somewhere between -1.4 and -1.3. Refining the input values one more time yields a solution between -1.34 and -1.33. 

Graphing Calculator Explorations
Solve the equation using algebraic methods. Solve it also by using graphing methods.  Use this numeric table method to show that {-3} is the solution to the equation . You will have to rewrite the equation in the form . Use the table method to solve the equation .  You should find three solutions.