Question

What is the range of the function defined by the equation y = x2 + 4x?

Answer 1

x for all real numbers

Answer 2

What does that mean?

Answer 3

y=x2 + 4x = (x+2)^2 - 4
therefore range of y is [-4,+infinity]

Answer 4

range tends to mean a span of things; in functions, the range is the span of outcomes possible

Answer 5

I think I understand, thanks so much! I appreciate it!

Answer 6

y=x2 + 4x = (x+2)^2 - 4
the minimum value of (x+2)^2 for any real value of x is 0
the maximum value of (x+2)^2 for any real value of x is +infinity
therefore range of y is [-4,+infinity]