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the function f(x) =
-x is shown on the graph.
which statement is correct?
the domain of the function is all real numbers greater
than or equal to 0.
the range of the function is all real numbers greater
than or equal to -1.
the range of the function is all real numbers less than or
equal to 0.
the domain of the function is all real numbers less than
or equal to 0.
-7-5-5-4-3-2-11
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7 x
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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

1. a^4+8a^3+24a^2+32a+16

2.y^8+8y^7+28y^6+56y^5+70y^4+56y^3+28y^2+8y+1

3.x^6-3x^4y^2+3x^2y^4-y^6