Question

what is the domain and range of f(x)=-2x^2-4

Answer 1

Given that f(x) is an elementary function with no discontinuity points, x can take any real value - so x can take values in (infinite,+infinite).

Studying lim of f(x) as x approaches infinity will yield -infinity.
Lim of f(x) as x approaches -infinity will also yield -infinity.
We may conclude that our f(x) is "coming" from -infinity and heading towards -infinity.

Aplying d/dx on f(x) we see that f'(x)= (-4)*x. By solving f'(x)=0 we find that one possible point of global/local maximum/minim is achieved in x=0.

By inputting x=0 in our function, we see that f(0)=-4.

Ergo we may conclude that f(x) is coming from -infinity (first limit) , "hits" a global maximum at x=0 in -4, and returns to -infinity. So the range of f(x) is (-infinity,-4].