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Find the equations of the horizontal and vertical asymptotes for the following. Tye none if the function does not have an asymptote.

a. f(x)=2x+3/x+2

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a. f(x)=2x+3/x+2

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As x approaches 0 from negative side, f(x) approaches - infinity. As x approaches 0 from positive side, f(x) approaches positive infinity.

The slope of tangent of f(x) = f '(x) = 2 - 3/x²

Slope approaches minus infinity as x tends to zero. f(x) is discontinuous at x=0.

__So the asymptote is x = 0 __as the tangent at x=0 (slope is infinity) is perpendicular to x axis.

f ' (x) = Slope approaches 2, as x tends to infinity. So there is an asymptote with slope equal to 2 as x tends to infinity. we have to find its equation.

f(x) as x tends to infinity is : 2 x + 2 + 3/infinity or 2 x + 2

the second asymptote is__ y = 2x + 2__

The slope of tangent of f(x) = f '(x) = 2 - 3/x²

Slope approaches minus infinity as x tends to zero. f(x) is discontinuous at x=0.

f ' (x) = Slope approaches 2, as x tends to infinity. So there is an asymptote with slope equal to 2 as x tends to infinity. we have to find its equation.

f(x) as x tends to infinity is : 2 x + 2 + 3/infinity or 2 x + 2

the second asymptote is