Lesson 12: Quiz - Solutions

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

Hello again, this is lesson 12, which explains the solutions to the questions in quiz one. After completing this lesson, you should understand the questions in the quiz and understand the solutions to those questions and be a better power learner of mathematics. In question one, you must decide which set of ordered pairs corresponds to the arrow diagram. From the diagram, we can see the following pairs of values. First there is zero and 14. Then we have zero and 24.

Then two and 14, two and 30 foreign 30 and finally 632 so for this arrow diagram, the correct set of ordered pairs is this one, which is option D. Question two asks us to identify the arrow diagram that corresponds to the table of values from the table lists the x values first like this. Now the y values Now we can add the arrows linking the pairs of values. Now you can see that this is option v. In question three, we must decide which equation represents the values given in the table. By looking at the table, we can see that for the first pair of values, negative For the y value equals negative two, the x value minus two. For the next pair of values, negative three, the y value equals negative one, the x value minus two, and then negative two, the y value equals zero, the x value minus two.

And generalizing, we can say that y equals x minus two, which is Option A. For Question four, we have to say which of the statements correctly explains why the values in the table represent a function. remind yourself of the definition of a function. It's a rule that connects each element of a first set with one and only one element of a second set. So looking at the table, you can see that each x value has only one y value. So the correct option is B.

Question five is similar to question four. Look carefully at the table. And remember the definition of a function. When x equals negative two, there are two y values two and negative three. So the relation is not a function, and the correct option is C. For question six, we must work out which relation is the correct one for the set of ordered pairs. Start by listing the x values.

Now the y values and add the arrows that link associated pairs of values. From the arrow diagram, we can see that when x equals negative seven, y has two values, negative five and two, which means that the relation is not a function, and the correct option is D. in question seven, we are asked to complete a statement that is essentially the definition of a function. So remember, a function is a rule in which each input value has only one output value. So that gives a as the correct option. For question eight, we have to decide which set of ordered pairs represents the equation y equals x squared. Now, the reason Really a special method for this question.

I expect you're familiar with the pattern of square numbers. One squared equals one, two squared equals four, three squared equals nine, and four squared equals 16. And so by inspection, we can see that this is option C. Now in question nine, we have to decide which of the sets of ordered pairs represents a function. remind yourself of the definition of a function. Each x value must have only one y value. So we'll check each set carefully.

In set A, the x value of two appears twice, each time with a different y value. So this is not a function. in set B, x equals one appears twice And with different y values, so this is not a function. And again, in set B, x equals two appears twice, also with different values of y. So this isn't a function either set C has x equals two appearing twice and with two different values of y. So now there is this a function.

Looking at set D, we can see that each x value has only one y value. So, it does represent a function and that means that the correct option is D. Finally, in question 10 decide which table of values does not represent a function. Again, remember the definition of a function, each x value must have only one one value. Now look at table B, the x value negative two occurs twice, and the corresponding y values are different. So the relation is not a function, and B is the correct option. That completes the solutions to quiz one.

How'd you get on with the quiz? 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 quiz once more. It's important to master these ideas

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