Question

please help due in 5 min!!! please help do all!!!

12 1. Let F(a)- (a) Determine any discontinuities of F(a) and classify them as either removable or nonre- movable. (b) Determine the any horizontal or vertical asymptotes of F(x). (c) Sketch a graph of F(x), indicating the asymptotes and any removable singular points. Be sure that you choose an appropriate scale.

Answer 1

$y=\frac{x^2-9}{x^2+7x+12}$

(r +3) (r-3)

(x +3) (x -3)

(x +3) (x -3) (r +4) (x +3)

(x +3) (x -3) (r +3) (x + 4)

to find discontinuities take denominator = 0

(r +3) (x +4)0

${\color{Red} x=-3, \:\:x=-4}$...............discontinuities of function

as we can see here (x+3) factor can be cancel out

so x=-3 is removable Discontinuity (at point x=-3 there is a hole)

and x=-4 is non removable Discontinuity

.

cancel the factor (x+3)

(r- 3) (r+4)

to find vertical asymptote take denominator = 0

$x+4=0$

${\color{Red} x=-4}$................ vertical asymptote

.

.

here degree of denominator and numerator are equal so horizontal asymptote is in the form of

$y=\frac{\mathrm{numerator's\:leading\:coefficient}}{\mathrm{denominator's\:leading\:coefficient}}$

$y=\frac{1}{1}$

${\color{Red} y=1}$.....................horizontal asymptote

10 y-1 horizontal asymptote 10 10 x-3 hole 10 x-4 vertical asymptote 15