The general form of rational function f(x) = N(x) / D(x) where N(x) and D(x) are polynomials. \ \

y = N(x) / D(x) \ \

In this case \ \

x < 2 , rational function is positive. \ \

Therfore y is positive. \ \

x > 2 , rational function is negative. \ \

Therfore y is negitive. \ \

horizontal asympotote is y = 0 \ \

Vertical asympotote is x = 2 \ \

Vertical asympotote x  = 2, horizontal asymptote y  =  0 . \ \

Vertical asympototes are found by D(x) = 0 \ \

So the denominator is x - 2. \ \

Next  find the polynomial N(x) : \ \

If the degree of the numarator is less than degree of the denominator  there is horizontal asympotote y = 0, which say x axis. \ \

numarator degree is 0. \ \

Possible numarator is N(x) = x ^0 (-1) \ \

N(x) is - 1 \ \

So far we have the rational function f(x) = - 1 / (x - 2)

Therfore the rational function f(x) = - 1 / (x - 2) \ \

Graph \ \

Draw the coordinate plane.

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