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Find the equations of the asymptotes of the function g(x) given by the equation (x+2)(y+3) = t.

Mathematics

ScanSolve AI Answer

1.1.1 The equations of the asymptotes of gg are derived from the given equation (x+2)(y+3)=t(x+2)(y+3) = t.
The vertical asymptote occurs when the term with xx is zero.
The horizontal asymptote occurs when the term with yy is zero.

Step 1: Identify the asymptotes from the equation.
For g(x):(x+2)(y+3)=tg(x): (x+2)(y+3) = t:
The vertical asymptote is x+2=0  ⟹  x=−2x+2=0 \implies x=-2.
The horizontal asymptote is y+3=0  ⟹  y=−3y+3=0 \implies y=-3.
The equations of the asymptotes are $\boxed

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