Consider the relation~ defined on Zx N = {(x,y) : x € Z, and y € N} by (a,b)~ (c,d) ad=bc. (a) Prove that is an equivalence relation. (b) List several elements of the equivalence class of (2,3). Repeat for the equivalence class of (-3,7). What do the equivalence classes have to do with the set of rational numbers Q? (c) Define operations and on Zx N by [(a,b)] → [(c,d)] = [(ad + bc, bd)], [(a, b)] [(c,d)]= [(ac, bd)]. Prove that and are well-defined. Try to do this question without using division! We will return to this example in the next section.

Describe the domain of the relationship shown here.

As I was driving along the highway to Cleveland, I noticed a speedometer check along the side of the road with posted signs 1 mile apart. I timed us and found that it took us 5 minutes and 45 seconds to travel 5 miles. We had the car set on cruise control, so we were traveling at a constant speed. A while later we passed a sign that said “Akron 76 miles.” At that speed, how long did it take us to drive those 76 miles to Akron? (Convert your decimal answer to an equivalent number of hours, minutes, and seconds. For example, 7.104 hours = 7 hours 6 minutes 14 seconds.)

Calculate and graph the domain of the following functions