1055 points 020 Submissions Used Given the rational function

-10.55 points 020 Submissions Used Given the rational function -223 1 13 Determine the follawing: (Answers should be integers or reduc DNE in the answer blank) a.) The vertical asymptote occurs at b.) The x-intercepts occur at the following x-coordinates: smallest value) largest value) c.) The y-intercept occurs at the y coordinate d.) The nonvertical asymptote occurs at e.) Which of the following best represents the graph of f(x)? fix)

Solution

(2x^2 -x - 15 )/(x-4)

a) Vertical asymtotes: Vertical asymptotes are vertical lines which correspond to the zeroes of the denominator of arational function.

(x-4) =0 ---> x=4

b) x intercepts:

2x^2 -x -15 =0

2x^2 -6x +5x -15 =0

2x(x -3) +5( x-3) =0

(2x+5)(x-3) =0

x = 3 ; x= -5/2

c) y intercept: plug x=0

y = (2x^2 -x - 15 )/(x-4)

= -15/-4 = 15/4

y = 15/4

d) Since the degree of the numerator is one greater than the degree of the denominator, I\'ll have a slant asymptote.

y = (2x^2 -x - 15 )/(x-4) = 2x +7

y = 2x +7