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.

Algebra ->  College  -> Linear Algebra -> 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.      Log On


   

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) About Me  (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.
++f%28x%29+=+%282x-1%29%2F%28x-5%29+++
Here's a graph (ignore the misbehavior around x=5, my graphing system is not great):
graph%28+400%2C+400%2C+-1%2C+10%2C+-10%2C+10%2C+%282x-1%29%2F%28x-5%29%29+
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: %282x-1%29%2F%28x-5%29=0 simplifies to 2%2F%28x-5%29=0
  • Text form: (2x-1)/(x-5)=0 simplifies to 2/(x-5)=0
  • Cartoon (animation) form: simplify_cartoon%28+%282x-1%29%2F%28x-5%29=0+%29
    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 highlight_red%28+%282%2Ax-1%29+%29%2F%28x-5%29=0.
Notes known roots (x-(0.5))
Look at highlight_red%28+%28highlight_red%28+2+%29%29%2F%28x-5%29+%29=0.
Remove unneeded parentheses around factor highlight_red%28+2+%29
It becomes highlight_green%28+2+%29%2F%28x-5%29=0.
Result: 2%2F%28x-5%29=0
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, -1%2F-5+=+1%2F5
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.
%282x-1%29%2F%28x-5%29 can be rewritten as
+%282x-1%29%2F%28x-5%29+=+%282%28x-5%29%2B9%29%2F%28x-5%29+=+2+%2B+9%2F%28x-5%29
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.