Question

Match the range of the function f(x) = x2 + 2x − 1 to its domain. Tiles 2 -2 3 -3 Pairs 2 14 7 -1

Answer 1

The domain is without restriction so x=(-oo, +oo)

The range has a minimum because this is a second order equation with a constant positive acceleration.

The minimum can be seen easiest by putting the equation into vertex form

y=x^2+2x-1

y+1=x^2+2x

y+1+1=x^2+2x+1

y+2=(x+1)^2

y=(x+1)^2-2  so the vertex is at the point (-1, -2), and this is the absolute minimum value for y or the range.  As x approaches positive or negative infinity, y approaches positive infinity:

y=range=[-2, +oo)