For the equation y = -(x+1)^2 + 4, determine the range?

Answer 1

A function is like a machine. The domain is what you can put into the machine without breaking it. The range is what you can get out of the machine.

In this case, we have basically 4 - something squared. Anything squared is either 0 or positive. So the most f(x) can be is 4 - 0 = 4 (when x = -1). But since the part that is squared can just keep getting bigger and bigger, f(x) will just get more and more negative. (Try x = 3 for example.)

So the range of the function is y <= 4.

Answer 2

Find the vertex: It's (-1, 4)

You can tell because the equation is written in standard form

(x-a)^2 +b or -(x-a)^2+b

Either way, the vertex is (a, b). Notice that you change the sign of the a but you leave the sign the same with b.

Since the leading coefficient is negative, the parabola opens downward so the range is everything below 4 (from vertex y-value)

So the range is (-infinity, 4] Lowen's right!

Answer 3

Been a while since I've done college algebra, but it looks like the range for this function is (-infinity,4]