First slide

Functions (XII)

Question

The range of the $y = \sqrt{9 - x^{2}}$ is

Easy

A

$[9, \infty)$
B

$(9, \infty)$
C

$[0, 3]$
D

$(3, \infty)$

Solution

$\sqrt{9 - x^{2}}$
$Least value of square root is 0 when 9 - x^{2} = 0 or x=±3$
$\begin{aligned} Also, greatest value of 9 - x^{2} is 9 when x = 0 . \\ Hence we have 0 \leq 9 - x^{2} \leq 9 \Rightarrow \sqrt{9 - x^{2}} \in [0, 3] \end{aligned}$

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