What are the asymptotes of y=1/(x−2)+1 and how do you graph the function?

Haiden Meyer

Haiden Meyer

Answered question

2022-09-28

What are the asymptotes of y = 1 x - 2 + 1 and how do you graph the function?

Answer & Explanation

Aniyah Liu

Aniyah Liu

Beginner2022-09-29Added 7 answers

1. Find the vertical asymptote by setting the value of the denominator(s) to zero.
x−2=0 and therefore x=2.
2. Find the horizontal asymptote, by studying the end behavior of the function. The easiest way to do so is to use limits.
3. Since the function is a composition of f(x)=x−2 (increasing) and g ( x ) = 1 x + 1 (decreasing), it is decreasing for all defined values of x, i.e. ( - , 2 ] [ 2 , ) . graph{1/(x-2)+1 [-10, 10, -5, 5]}

lim x 1 x - 2 + 1 = 0 + 1 = 1
Vertical: x=2
Horizontal: y=1

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