How do you find vertical, horizontal and oblique asymptotes for #-7 / (x+4)#?

1 Answer
Mar 21, 2018

Answer:

#x=-4#
#y=0#

Explanation:

Consider this as the parent function:

#f(x)=(color(red)(a)color(blue)(x^n)+c)/(color(red)(b)color(blue)(x^m)+c)# C's constants (normal numbers)

Now we have our function:

#f(x)=-(7)/(color(red)(1)color(blue)(x^1)+4)#

It's important to remember the rules for finding the three types of asymptotes in a rational function:

Vertical Asymptotes: #color(blue)("Set denominator = 0")#

Horizontal Asymptotes: #color(blue)("Only if "n = m, "which is the degree." " If " n=m, "then the H.A. is " color(red)(y=a/b))#

Oblique Asymptotes: #color(blue)("Only if " n > m " by " 1, "then use long division")#

Now that we know the three rules, let's apply them:

V.A. #:#

#(x+4) = 0#
#x=-4# #color(blue)(" Subtract 4 from both sides")#
#color(red)(x=-4)#

H.A. #:#

#n != m# therefore, the horizontal asymptote stays as #color(red)(y = 0)#

O.A. #:#

Since #n# is not greater than #m# (the degree of the numerator is not greater than the degree of the denominator by exactly 1) so there is no oblique asymptote.