You can
put this solution on YOUR website!In a problem that I solved earlier this evening, I made the observation that solving inequalities can most easily be solved by graphing calculator methods. Perhaps you were the one who asked that question.
First of all, you must set the inequality to zero:
? What you need to graph is this:
and determine, since the inequality you are solving is <=, what values of x are ON OR BELOW the X-AXIS. In the previous example, the inequality was a < symbol, so we had to solve for all values that are BELOW the X-axis. Because this one is <=, we need to include values ON the x-axis as well as BELOW it.
The first step is to graph
. As I said, because the problem says <=0, you need to find all values of x for which the graph is ON or BELOW THE X-AXIS!
So here is the graph:
Notice from thiss graph that the values of y are BELOW the x-axis for
. The endpoint at x= 0 cannot be included since it makes the function undefined. The final answer is
, which in interval notation is (-infinity, 0).
This may not have been what you were expecting in a problem. I think it's MUCH easier than the old ways that I used to teach.
R^2 at SCC
