Hello again, this lesson continues with the full solutions to question six to 10 of activity to after completing this lesson, you should understand the questions in activity to understand the solutions to these questions and be a better power learner of mathematics. Let's look at question six is the relation represented by the equation y equals three to the power x a function to some values for x, I chose negative two, negative 101 and two, but of course you may choose different values. If you want Use the equation to calculate the corresponding values for y. So when x equals negative two, y equals three to the power negative two, which is one over nine, or one ninth. When x equals negative one, y equals three to the power negative one, which is one over three, or one third. When x equals zero, y equals three to the power zero, which everyone knows is equal to one.

Next, when x equals one, y equals three to the power one, or simply the value three. And finally, when x equals two, y equals three to the power two, which is nine. We can see that for each x value, there is One and only one y value. So the relation is a function. Question seven is similar to question six, but the equation is y equals three over x. And we must decide whether this is a function or not.

Once again, let's choose some values for x, negative three, negative two, negative 1012, and three. And again, you may choose other values if you prefer. Now use the equation to calculate the values of y when x equals negative three, y equals negative one, when x equals negative two, y equals negative three over two, when x equals negative one, y equals negative three, when x equals zero Then y equals three over zero. And I'm sure you remember that division by zero is not allowed. Or more mathematically, we say it's undefined. When x equals one, y equals three, when x equals two, y equals three over two.

And lastly, when x equals three, y equals one, we can see from the table that for each value of x, except zero Of course, there is only one y value, which means that this relation is a function. Question eight. We have a set of ordered pairs and have to say whether the relation is a function or not. Examine the ordered pairs carefully. Do you notice anything particular and what is the definition of a function? We can see that when x equals four, y has two different values, two and negative two.

So this relation is not a function. Another way to do this question is to notice that when x equals one, y also has two different values one and negative one, which also tells us that the relation is not a function. Now in question nine, which is similar to question eight, is the relation represented by this set of ordered pairs, a function or not? As we've done before, look carefully at the ordered pairs. Do you notice anything? And what is the definition of a function?

Looking at the ordered pairs, you can see that each x value has one and only one y value. So these ordered pairs do represent a function. Now question 10 is also similar to questions eight and nine. Do these ordered pairs represent a function or not? So check the ordered pairs. See if there's anything special.

And recall the definition of a function. It's not hard to see that each x value has one and only one y value. So once more, this relation must be a function. That completes the solutions for activity two. 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 again at the minute Serial and try the questions once more. I'm sure you can do it.