How do you graph f(x)=2x1 using holes, vertical and horizontal asymptotes, x and y intercepts?

1 Answer
Oct 14, 2017

No holes.
Vertical asymptote: x=1
Horizontal asymptote: y=0
No x intercepts.
y-intercept: 2

Explanation:

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
x1=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 x02 gives 2. Denote this as n
For d(x), the degree is 1 (since x1). 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=2x1
There are no x intercepts.

To find the y intercept, plug in 0 of x and solve for y.
f(x)=201
f(x)=2
The y-intercept is 2.

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