the graph shown has
vertical asymptotes x = -1 , x = 2
horizontal asymptote y = 1
x intercept -2 , 3
y intercept 3
vertical asymptotes occur in denominator
x intercepts occur in numerator
horizontal asymptote is leading coefficinet of numerator / leading coefficinet of denominator
so, function is
y = a( x + 2) ( x - 3) / (x+1) (x-2)
plugging y = 3 and x = 0
3 = a ( 2 * - 3) / ( 1* - 2)
a = 1
y = {( x + 2) ( x - 3)} / {(x+1) (x-2) } |
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