SOLUTION: Identify any intercepts and asymptotes of the following: f(x)=2x-1/x-5 I got 1 and 2 as asmptotes, is that right? I also don't know how to find intercepts.

Question 5841: Identify any intercepts and asymptotes of the following:
f(x)=2x-1/x-5
I got 1 and 2 as asmptotes, is that right?
I also don't know how to find intercepts.
Answer by ichudov(507) (Show Source): You can put this solution on YOUR website!
I am going to GUESS what you meant. I suspect that you did not use parenthese properly. If my guess is wrong, please submit the problem again.

Here's a graph (ignore the misbehavior around x=5, my graphing system is not great):

to find x-intercept, remember that x intercept means that the function is equal to zero. that's a simple equation:

Solved by pluggable solver: EXPLAIN simplification of an expression

Your Result:

YOUR ANSWER

This is an equation! Solutions: x=0.5.
Graphical form: simplifies to
Text form: (2x-1)/(x-5)=0 simplifies to 2/(x-5)=0
Cartoon (animation) form:
For tutors: simplify_cartoon( (2x-1)/(x-5)=0 )
If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at .
Notes known roots (x-(0.5))

Look at .
Remove unneeded parentheses around factor highlight_red%28+2+%29

It becomes .
Result:
This is an equation! Solutions: x=0.5.

Universal Simplifier and Solver

Done!

so, 1/2 is the x intercept. Y intercept is the value of function with x set to zero,
Asymptote is not a hard thing to find. You have two polynomials dividing one another, the asymptote is the fraction of the top highest coefficient to bottom highest coefficient, or 2/1, or 2.
can be rewritten as

the last part obviously is composed of two things, constant 2 and a part that approaches 0 as x tends to infinity. So 2 is the asymptote.
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