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What is the Domain and range?

Domain:

Domain in interval notation:   [0, infinity)

This is because the domain is the set of all allowed x inputs. In this case, x = 0 is the smallest and we include this endpoint. Any x value x = 0 or larger is part of the domain (since the graph stretches' on forever to the right)

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Range:  

Range in interval notation:   [2, infinity)

For similar reasoning as the domain, but now we consider the possible y output values. Here y = 2 is the smallest and we include it. Note the square bracket for interval notation means "include this endpoint". The curved parenthesis means "exclude this endpoint"

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4