Question

a. Determine whether the relation represents y as a function of x. y=x2b. Determine whether the relation represents y as a function of x. x2+y2=4

Answer 1

a. Is a function

Since a function is a relationship where to each value of x corresponds a single value of y. In this case:

`y=x^2`

Then for every value of x, a single value of y corresponds it.

b. Is not a function.

Following the same logic as before, let's take the relationship and let y alone on the left hand side:

`\begin{gathered} y^2+x^2=4 \\ y^2=4-x^2 \end{gathered}`

Now, we can apply square root on both sides, but we must remember that the square root has two values: a positive one and a negative one.

This is because fi we ask wich number solves y² = 9 we have two answers: (-3)·(-3) = 9 and 3·3 = 9

Thus, we must add a plus/minus sign:

`y^2=4-x^2\Rightarrow y=\pm\sqrt[]{4-x^2}`

And now we can see that for each value of x, we get two different values of y:

`\text{ Let's grab }^{}x=0\colon y=\pm\sqrt[]{4-0^2}=\pm\sqrt[]{4}=\pm2`

Then for a value of x = 0 we get y = -2 and y = 2, then this is not a function.