Problem 1 Find all zeros and vertical asymptotes of the rati

Problem #1

Find all zeros and vertical asymptotes of the rational function

- The function has vertical asymptote(s) when x=__________

-The function has horizontal asymptote(s) when y=____________

Problem #2

Estimate the one-sided limits below.

Problem #3

Consider the function:

If this function has a horizontal asymptote, give its there is no horizontal asymptote type

y=______________

Find the y-intercept

y=______________

f(x) = (x^3 -27)/(-x^3 -27x)

Vertical asymtote : plug -x^3 -27x =0

x=0 ; -x^2 -27 =0 ---> x^2 = -27 (imaginary)

So, x= 0 is the vertical asymtote

Horizontal asymtote: degree of both num and den are same so : y = x^3/-x^3 = -1

y = -1

3) f(x) = (7x +9)(2x+5)/(2x -8)(4x+2)

Horiaonal asymtote : as degree of num, and den, are same so, horizontal asymtote is ratio of coeffcientof highets degree terms.

y = 14x^2/8x^2 = 14/8 = 7/4

y = 7/4

y intercept: plug x=0 ; y =( 9*5)/-8*2 = -45/16

y= -45/16