Question

Find the domain and range of the function y = √x-3 + 6

Answer 1

Domain:
`[3,\infty)`

Range:
`[6,\infty)`

Explanation:

I assume you mean
`y=√(x-3) +6`?

Take note of how x cannot be less than 3 because it would result in a negative number under the radical, which isn't real. However, x CAN be 3 because
`√(3-3)+6=√(0)+6=0+6=6` which is real.

Therefore, the domain of the function is
`[3,\infty)`

As for the range of the function, we saw previously that the minimum of the domain resulted in the minimum of the range, which was 6.

Therefore, the range of the function is
`[6,\infty)`

See attached graph below for a visual.