What are the domain and range of this function, and how would I graph it?

Question

f(x) = -5 + sqrt(9-x^2)

I need to find the domain, range, and sketch a graph.

Any help would be appreciated. For the graphing, if you could just explain that would help. Please be as thorough as possible so that I can do similar problems on my own. Thanks so much and 10 points to the best answer!

Answer 1

y=-5+√(9-x^2)

1) Domain

9-x^2≥0 ==> 9≥x^2 ==> |x|≤3 ==> -3≤x≤3

Domain=[-3,3]

2) Range

⋆ The easier way:

x=0 ==> y=-5+√(9-0)=-5+3=-2

x=±3 ==>y=-5+√(9-9)=-5

Range=[-5,-2]

⋆⋆ The harder way:

y+5=√(9-x^2)>0..............(1)

(y+5)^2=9-x^2

x^2+(y+5)^2=3^2.............(2)

This is an equation of a circle with center at (0,-5) and radius r=3.

From (1) and (2) ==>

f(x)=-5+√(9-x^2) is the upper half of that circle ==>

ymin=-5, ymax=-5+3=-2

Range=[-5,-2]

3) Graph: The upper half of the circle with center at (0,-5) and radius r=3.

http://i299.photobucket.com/albums/mm286...