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

blogswput 2022-09-12 Answered
How do you graph f ( x ) = x x - 2 using holes, vertical and horizontal asymptotes, x and y intercepts?
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Answers (1)

trestegp0
Answered 2022-09-13 Author has 12 answers
f ( x ) = x x - 2
f ( x ) = ( x - 2 ) + 2 x - 2
f ( x ) = 1 + 2 x - 2

As x , y 1
ie As x approaches a very big number, 2 x - 2 will become 0
For the vertical asymptote, x - 2 0 since the denominator cannot equal to 0.

Therefore, there is a horizontal asymptote at y=1 and a vertical asymptote at x=2

For intercepts,
When y=0, x=0
When x=0, y=0

Then, after plotting your intercepts and your asymptotes, you can hopefully see the outline of your graph. Your end points should be approaching the asymptotes but never touching your asymptotes.
graph{x/(x-2) [-10, 10, -5, 5]}

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