Domain and Range?!?!?

Question

Use a graph to find the range of the function on the given domain.

f(x)= sqrt(9-x^2), -3 <= x <= 1 (this is the domain)

Can you explain how to find the range?!? I got like 0 <= y <= 3

Any help would be much appreciated.

Answer 1

x^2 + y^2 = 9 is a circle of radius 3 centred at the origin.

This equation gives:

y^2 = 9 - x^2.

Writing f(x) = sqrt(9 - x^2) implies f(x) is never negative. That restricts the portion of the graph to the upper semicircle.

The restricted domain - 3 &lt;= x &lt;= 1 restricts the graph to a portion of the upper semicircle between x = - 3 and x = 1.

The y values which occur over that domain range from 0 to 3,  making the range [0, 3].