How do you graph f(x)=2/(x−1) using holes, vertical and horizontal asymptotes, x and y intercepts?

albiguguiismx

albiguguiismx

Answered question

2022-09-08

How do you graph f ( x ) = 2 x - 1 using holes, vertical and horizontal asymptotes, x and y intercepts?

Answer & Explanation

Sugainkohr

Sugainkohr

Beginner2022-09-09Added 13 answers

Denote f(x) as n ( x ) d ( x )

There are no holes since there are no common factors.

To find the vertical asymptote,
Solve d(x)=0
x - 1 = 0
x=1

Therefore the vertical asymptote is x=1.

To find the horizontal asymptote,
Compare the leading degree of n(x) and d(x).

For n(x), the degree is 0, because x 0 2 gives 2. Denote this as n
For d(x), the degree is 1 (since x 1 ). Denote this as m

When n<m, the x-axis (that is, y=0) is the horizontal asymptote.

To find the x intercept, plug in 0 for y and solve for x.
0 = 2 x - 1
There are no x intercepts.

To find the y intercept, plug in 0 of x and solve for y.
f ( x ) = 2 0 - 1
f(x)=−2
The y-intercept is −2.

graph{2/(x-1 [-100, 100, -5, 5]}

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