Question

Help reciprocal functions and holes?

Answer 1

I need to find:
a) Excluded values
b) y intercept
c) x intercept
d) horizontal asymptote
e) vertical asymptote
f) holes

Answer 2

for the following: f(x) \[(x^2+x-6)/(-4x^2-16x-12)\]

Answer 3

I got up to:
a) -1, -3
b) (0, 1/2)
c) (2,0) (-3,0) ??? what happens with the hole? is it an x int? or not?
d) (0, -1/4)
e) x=-1, x=-3???
f) the hole is (-3, -5/8)

Answer 4

A zero in the denominator is a vertical asymptote UNLESS it is also a zero of the numerator.

Show numerator and denominator factored completely. We can talk from there.

Answer 5

i got to the part where it's: (x+3)(x-2)/-4(x+1)(x+3)

Answer 6

and the x+3 would cancel out

Answer 7

making it (x-2)/-4(x+1)

Answer 8

Don't be so cancel happy. We may need that information.

a) Excluded values From the Denominator x = -1 and x = -3 You have this, but your notation could use some improvement.

b) y intercept (0,1/2) Substituting x = 0. Very good.

c) x intercept The numerator suggests (2,0). You are done, here. You may be tempted to write (-3,0), but don't do it. Look at part a. x = -3 is already excluded.

d) horizontal asymptote The horizontal asymptote is an equation of a line. You have a point. Had you written y = -1/4, you would have been correct.

e) vertical asymptote x = -1. very good. You are done, here. Again, you may be tempted to write x = -3, but don't do it. Look at part a. x = -3 is already excluded.

f) holes Pretty obviously that annoying x = -3 and wherever it would land on the reduced version.

Answer 9

Thank you very much!!

Answer 10

The important thing to remember is that the reduced function and the original function are EXACTLY the same EXCEPT for x = -3. They differ in that one place.