Question

Determine whether the formula describes y as a function of x. Explain your reasoning.

y = -3x^2 - 7x - 6

Answer 1

@agent0smith

Answer 2

It does. For any number value that you choose x to have, you get a y value in a well-defined way: by doing the arithmetic.

Answer 3

y = -3x^2 - 7x - 6
Put any value for x and you get just one value for y (not multiple y values).
Each x maps to just one y value.
Therefore, it is a function.

Another approach:
y = -3x^2 - 7x - 6 is a parabola that opens downward.
Any vertical line will intersect the parabola at just one point.
It passes the vertical line test.
Therefore, it is a function.

Answer 4

aum, why does it intersect at just one point?

Answer 5

Draw a parabola that opens downward and draw a vertical line at any x. It will intersect the curve just once and not multiple times which implies each x maps to just one y. Therefore, it is a function.