# Give the equation of the function pictured. Explain how you got your answer.?

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- alexLv 71 month ago
Hint:

oblique asymptote y = (1/4)x + 1/2

graph

y=(1/4)x + 1/2 +(ax+b)/[(x+2)(x-1)]

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- ted sLv 71 month ago
3 asymptotes , x = - 2 , x = 1 , y = ( x + 2 ) / 4 { line equation } ; zeros at x = - 3 & x = - 1 ; passes through ( 3 , 2)............so on the bottom (x + 2)(x - 1) are needed ; on the top are ( x + 3) (x + 1 ) ; top has to be one degree higher than the bottom so one of the factors has to have a power increased..so far : y = [ (x + 3) ( x + 1)² ] / [ ( x + 2 )(x - 1 ) meets the condition ;to go through 9 3 , 20 we need to multiply by 5/ 9.....y = [ 5 ( x + 3)(x+1)²] / [ 9 ( x + 2 )(x - 1) ]...but this does not have the line asymptote......will come back later

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