if f(x)=sqroot (4-(x^2)) then the domain is (-infinity,4] right?
how can I get the range without sketching?

Question

if f(x)=sqroot (4-(x^2)) then the domain is (-infinity,4]  right?
how can I get the range without sketching?

anonymous · Answer

First the domain is not (- infinity 4). It is [-2,2].

anonymous · Answer

The range is [0,2]. You can say that since x lies in [-2,2] and the function returns same value for x and -x. Minimum is at x=2. and max at x=0

anonymous · Answer

you got the domain wrong. 
the domain of sqroot is [0,+inf) thus 4-(x^2)>=0  so  x^2 <= 4  so 
$$x \le \pm 2$$

anonymous · Answer

sqroot is continuous function so if you find min and max of 4-x^2 while considering the domain and sqroot it - you will find your range

anonymous · Answer

oh yes you are right i got the domain from x^2<= 4  thanks  a lot  not x

anonymous · Answer

the min/max of the function in sqroot are 0 and 4 respectively thus your range is [0,2]

anonymous · Answer

thank you so much

anonymous · Answer

something to note about this type of questions is that sketching helps. if you draw a quick sketch of the y=-x^2+4 parabula ("sad" parabula because of the negative sign in front of x^2 with its peak at (0,4) )

anonymous · Answer

you are 100% right visual calculus is very helpful , thanks for the tip really appreciate it