15. Identify the rational function represented by the graph a) c) 16. Determine

Question

15. Identify the rational function represented by the graph a) c) 16. Determine x-intercepts, y-intercepts, horizontal asymptotes, vertical asymptotes and holes for the given rational function, if any +x-6 a) x-int. x 0; y-int: none; horiz asymp: none; vert. asym: x 2; holes : x 3 b) x-int. : none; y-int: none: horiz asymp: y-1: vert. asym: x 2; holes : x-3 c) x-int. : x-0; y-int: y-0: horiz asymp: y : 1 ; vert. asym: x-2; holes at x--3 d) x-int. : x =-3; y-int: y =-6; horiz asymp: y = 2; vert. asym: x 1: holes: none +212+4 2x2+1 For the rational polynomial i) Explain if a horizontal or slant asymptote exists li) Find the equation of the line for the asymptote indicated in ().

Explanation / Answer

15) the function has 2 zeros

x = -2 , x = +2

so top expression would be

(x -2) ( x+2) = x^2 - 4

vertical asymptotes are x =-3 , +3

bottom expression is

(x-3)(x+3) = x^2 - 9

hence , the function is

(x^2 - 4 ) / (x^2 - 9 )

option c is correct

16) (x^2 + 3x ) / ( x^2 + x - 6 )

x intercepts are

x^2 + 3x =0

x(x+3) = 0

x =0

vertical asymptotes are

(x +3) (x-2) = 0

x = 2

holes = x = -3

horizontal asymptote y =1

y intercept = 0

option c is correct

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