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functions and asymptotes
- Thread starter MaryM
- Start date
Hello, MaryM!
The simplest is: .\(\displaystyle f(x) \:=\:\dfrac{a}{x-3}\;\;\text{ for any real }a \ne 0\)
If f(x) has a horizontal asymptote at y = 0 and a vertical asymptote at x = 3,
. . find an equation for the function.
The simplest is: .\(\displaystyle f(x) \:=\:\dfrac{a}{x-3}\;\;\text{ for any real }a \ne 0\)
D
Deleted member 4993
Guest
A little more complicated is:
\(\displaystyle f(x) \ = \ \dfrac{a}{(x-3)^n} \ \ \text {for any real} \ a \ \ne \ 0 \ and \ n \ > \ 0\)
.
\(\displaystyle f(x) \ = \ \dfrac{a}{(x-3)^n} \ \ \text {for any real} \ a \ \ne \ 0 \ and \ n \ > \ 0\)
.
If f(x) has a horizontal asymptote \(\displaystyle > > \)at \(\displaystyle < < \)y=0 and a vertical asymptote \(\displaystyle > > \)at\(\displaystyle < < \) x=3
find an equation for the function
MaryM,
replace each "at" with "of." You are stating equations of lines, and you
are further indicating that they are asymptotes.
The horizontal asymptote doesn't occur at y = 0. The horizontal asymptote \(\displaystyle is\)
y = 0.
The same idea is true for the vertical asymptote.