Hello, welcome to lesson nine, which contains the full solutions to questions one to five of activity two. After completing this lesson, you should understand the questions in activity to understand the solutions to the questions in activity two, and be a better power learner of mathematics. Here's question one. We have to decide if the relation shown by the table of values is a function or not. And we must give a reason for our answer. Start by looking carefully at the table.

Do you notice anything unusual? recall the definition of a function We can see from the table that for each x value, there is one and only one y value. So this means that the relation must be a function. Question two is similar to question one, decide if the relation as shown by the table of values is a function or not. And again, give a reason for your answer. Now, check the table carefully, what do you notice, remind yourself of the definition of a function.

In the table, we can see that the x value of two occurs twice and that the y values are both different negative three and one. This means we can say that the relation is not a function. Now we could do this in a different way. Notice that The X value of naught point five also appears twice in the table. And its corresponding y values are also different. Negative two and zero.

So this means the relation is not a function. Now in question three, we have a relation shown by an arrow diagram. And we must say whether this is a function or not, and give a reason. So, examine the diagram carefully to see if there's anything special about it and remind yourself of the definition of a function. We can see that for each input value, there are two output values a with E and F, A, B with D and F and C with D and E. So, this relation is not a function For Question four, we have to decide if the relation represented by the ordered pairs that satisfy the equation. two x minus y equals 11 is a function.

Start by choosing a few values of x. I chose negative four, negative 202, and four, but you could choose other values if you wish. Now we use the equation to calculate the corresponding y values, but first, it will be convenient to transpose the equation. So if we have two x minus y equals 11, we can rewrite it as y equals two x minus 11. Now, when x equals negative four, y equals negative 19 when x equals negative two, y equals negative four 15 when x equals zero, y equals negative 11, when x equals two, y equals negative seven. And finally, when x equals four, y equals negative three, we can see from the table of values that there is one and only one y value for each x value. So we can say that this relation is a function.

Question five is similar to question four, but with a different equation. Y equals X squared minus one. As before, choose some x values. These are mine, negative two, negative 101 and two, but again, you could use other numbers if you want. Now we use the equation to calculate the y values in the table when x equals negative two, y equals three, when x equals negative one, y equals zero. When x equals zero, y equals negative one, when x equals one, y equals zero.

And lastly, when x equals two, y equals three. Once again, we can see from the table, that for each value of x, there is one and only one value of y. So the equation y equals x squared minus one represents a function. So that completes the solutions to questions 125 you're halfway now? How are you doing so far? I do you hope things are going well.

Please go to the next video for the solutions to question to six to 10