Activities 2a and 2b

We don't hit the topic about solving inequalities until later in the course, but in order to find the domain of a function you need to be able to solve some simple inequalities and to simplify some simple intervals.

When the book asks you to find the domain, they are really asking you to find the largest subset of the real numbers that when plugged in to your function gives you a real result. Thus your answer should be all reals minus whatever will not give you a real result. For the functions you have learned about so far, the only things we need to throw out are numbers that make a denominator zero and numbers that make an even root negative. Thus if we have a function such as we need to make sure that 5 and -5 is not in our domain since they would make the denominator zero and we need to make sure that 4-x ≥ 0 which means 4 ≥ x or x ≤ 4. Therefore our domain is: (-inf, -5)U(-5, 4]. Notice I solved a simple inequality and I simplified my answer. I don't want to leave the answer as x £ 4 and x ¹ ±5.

Activity 2a: For 5 points of your online grade, solve the following simple inequalities and write your answer in simplified interval notation.  Show or explain any work that you did to solve them.  Some of you may want to graph a portion of your problem to determine where the expression is ³ 0.

Activity 2b: Make up a real valued function whose largest real domain is the same as your answer to activity 2a. This is worth 5 points and it is alot easier than you think. Just look at the problem in my example above and think of it backwards.

If you find that you are having difficulties, try e-mailing someone with a problem similiar to yours. Maybe you can work together.