What are the asymptotes of y=1/(x-2)+1 and how do you graph the function?
1 Answer
May 15, 2017
Vertical:
Horizontal:
Explanation:
- Find the vertical asymptote by setting the value of the denominator(s) to zero.
x-2=0 and thereforex=2 . - Find the horizontal asymptote, by studying the end behavior of the function. The easiest way to do so is to use limits.
- Since the function is a composition of
f(x)=x-2 (increasing) andg(x)=1/x+1 (decreasing), it is decreasing for all defined values ofx , i.e.(-oo,2]uu[2,oo) . graph{1/(x-2)+1 [-10, 10, -5, 5]}
Other examples:
What is the zeros, degree and end behavior of