Lesson 6: Activity 1 Solutions #6-10

The Basics of Relations and Functions Section 2: Relations and Functions
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Transcript

Hello again, this lesson continues with the solutions to activity one. After completing this lesson, you should understand the questions in activity one, understand the solutions to those questions and be a better power learner of mathematics. Let's look at question six. This time we start with a table of values and have to draw it arrow diagram. Check the table ah to have the y values are the same three. And yes, I remember what an arrow diagram is.

This the first element of each pair using the x values, zero, naught point two naught point four naught point six and naught point eight. Now list the second element of each pair using the y values 1.4 2.43, which is twice in the table and once in the diagram, and 3.2. Now complete the diagram with the relevant arrows like this. So the solution is the table of values and its arrow diagram. Now, in question seven, we're given an arrow diagram and have to draw the corresponding table of values. The first thing to do is to look carefully each element in the first set, that's a, b and c is related to two elements in the second set.

There's D, E and F. And do you remember What a table of values is. So we need a table with two rows and six columns. Take the elements and add them to the table like this. A and E, A and F, B and D, B and F, C and D, and C and D. And there's the solution, the arrow diagram, and it's table of values. In question eight, this is something different. A single set of values and a relation which is, is a divisor of, and we must write down a set of ordered pairs.

Let's make sure we understand the question. There are four elements in set A, the numbers 235 and six. The relation is a divisor of means that for two Numbers, say four and 12. We say that four is a divisor of 12. Now we can answer this question in more than one way. An easy way is to test each pair of numbers to see if they satisfy the relation.

We'll do it that way. First. Let's start with the number two. We'll check it against each of the other numbers. Is to a divisor of three. No, it isn't.

Is to a divisor of five. No, it isn't. Is to a divisor of six? Yes, it is. So that gives us the ordered pair, two and six. And don't forget to check is two a divisor of itself.

Yes, of course it is. So the ordered pair is two and two. Now check. Three with five and six is three divisor of five? No, it isn't. is three a divisor of six?

Yes it is. So the ordered pair is three and six. And what about three as a divisor of itself? Yes again. So we have an ordered pair three. Now check.

Five and six is five a divisor of six. No. is five a divisor of five? Yes it is. So we have an ordered pair five and five. And finally is six a divisor of six?

Yes, it is. And the ordered pair is six and six. Combining this information gives us our set of ordered pairs, as you see here, two and two, two and six, three and three, three and six, five and five, and six and six. Now you could of course, start by drawing the arrow diagram to show the relation is a divisor of. And finally ordered pairs from there, as you see here. Question nine is different again, we have two sets, a and b. a relation is a factor of that we must draw a table of values.

We can answer this question in more than one way. But we'll start with the arrow diagram. lists the elements of set a like this. Now lists the elements of set B here. Add the arrows that correctly show the relation is a factor of, for example, two is a factor of 12. Four is a factor of 20 and so on, with all the other values Now draw the table of values that corresponds to this diagram.

And here it is. Finally, in question 10, we're given a table, and we asked to draw the arrow diagram. But there's one extra task, find any equation that represents the relation. Now you should be able to check the table for anything special, and remind yourself of what an arrow diagram is. As we've done before, this the x values, negative two negative 101 and two, and the y values 2345 and six and draw the arrows between the pairs of corresponding values. Now we must look for a pattern between the x and the y values.

Can you see that two a y value equals negative two, an x value plus four and three, a y value equals negative one, the x value plus four. And again, for the y value equals zero, the x value plus four and we can generalize y equals x plus four. So this gives us our solution, the arrow diagram and the equation we just worked out. That completes the solutions to activity one. How did you get on with this activity? Did you achieve at least eight correct out of the 10 questions?

Well done if you did, if you didn't quite make it, look over the material again and try the questions. Once more, I'm sure you can do it.

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