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What is the domain and range of #f(x) = sqrt (9 - x^2)#?

Answer 1

Domain: #[-3,3]#
Range: #[0,3]#

A square root cannot have a negative value; otherwise, the solution is fictitious.

So, we need #9-x^2\geq0#, or #9\geqx^2#, so #x\leq3# and #x\geq-3#, or #[-3.3]#.

As #x# takes on these values, we see that the smallest value of the range is #0#, or when #x=pm3# (so #sqrt(9-9)=sqrt(0)=0#), and a max when #x=0#, where #y=\sqrt(9-0)=sqrt(9)=3#

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Answer 2

Eva Abramson

Domain: (-3 \leq x \leq 3) Range: (0 \leq f(x) \leq 3)

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.