Determine whether the equation defines y as a function of x.

Question

y = 2x^2 + 6x +9

Answer 1

y=2x² + 6x + 9.

Choose several values of x and solve for y.

Let x=-3, -2, -1, 0, 1, 2, 3.

2(-3)² + 6(-3) + 9 = 18 - 18 + 9 = 9.

2(-2)² + 6(-2) + 9 = 8 - 12 + 9 = 5.

2(-1)² + 6(-1) + 9 = 2 - 6 + 9 = 5.

2(0)² + 6(0) + 9 = 0 + 0 + 9 = 9.

2(1)² + 6(1) + 9 = 2 + 6 + 9 = 17.

2(2)² + 6(2) + 9 = 8 + 12 + 9 = 29.

2(3)² + 6(3) + 9 = 18 + 18 + 9 = 45.

For every value of x, y takes on exactly one value, so y is a function of x.

Answer 2

The uniqueness of y values has nothing to do with the question of whether y is a function of x.

It’s the other way around: if there is only one y value for each specific value x , then y is a function of x.

So I agree with Nestor R.’s argument: since no value value of x can result in more than one value of y, y is a function of x.

Answer 3

You can look at it and tell.

Let's say it was just y = 2x² + 9. You could say x = 3 or x = -3 and come up with the same y, because squaring any number results in a positive number.

Because we have the + 6x, though, x = 3 or -3, for example, would result in different y's.