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.
