I need someone to help me answer this difficult problem for me. This is important for me so I would appreciate if everything is clear for me to understand. Thanks!

(a) Find lim *f(x)* and state which shortcut rule was used:

*x*→-∞

(b) Find the equation of any horizontal asymptote:

(c) Find the *y*-intercept:

(d) Use algebra to find the equations of any vertical asymptotes and the coordinates of any holes (removable discontinuities).

(e) Find the *x*-intercept:

(f) Sketch a graph for *f(x)* showing the results from parts (a) through (e). Set up the graph for *x*-values from -8 to 8 with increments of 1 and *y*-values from -18 to 18 with increments of 2.

GAMEMASTERX40 Apr 4, 2020

#2**+2 **

f(x) = (-4x^{2} -4x + 48) / (2x^{2} - 10x + 12)

a) Divide both the numerator and denominator by x^{2} ---> (-4 - 4/x + 48/x^{2}) / (2 - 10/x + 12/x^{2})

as x approaches infinity, every term with an x in the denominator goes to zero; so ---> -4/2 = -2

b) Horizontal asymptote: y = -2

c) y-intercept: x = 0 ---> y = 4

d) Factor the numerator: -4x^{2} - 4x + 48 = -4(x^{2} + x - 12) = -4(x + 4)(x - 3)

Factor the denominator: 2x^{2} - 10x + 12 = 2(x^{2} - 5x + 6) = 2(x - 2)(x - 3)

Since both the numerator and denominator has a factor of 3, a removable discontinutity occurs at x= 3

A vertical asymptote occurs at x = 2.

e) x-intercept: y = 0 ---> x = -4

geno3141 Apr 4, 2020