anonymous
  • anonymous
How to find the intercepts and asymptotes of f(x)=2x^2+x-2/x^2-1
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Is the function\[f(x)=\frac{ 2x^2+x-2 }{ x^2-1}\]
anonymous
  • anonymous
yes
anonymous
  • anonymous
OK lets start with intercepts. What is the interception with y-axis? Isnt it when x=0?

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anonymous
  • anonymous
sorry, intercept with y-axis
anonymous
  • anonymous
yeah
anonymous
  • anonymous
so, what is the value of f(x) when x=0?
anonymous
  • anonymous
f(0)=2(0)^2+0-2/(0)^2-1=-2/-1=2
anonymous
  • anonymous
Perfect! Now The x-axis crossing! Arent they the values of x that make y=0? And arent the values that make y=0 the same values that make the numerator=0?
anonymous
  • anonymous
so I have to get the numerator equal to zero
anonymous
  • anonymous
Bingo!
anonymous
  • anonymous
so 0=2x^2+0-2, how can I solve that
anonymous
  • anonymous
i meant +x not +0
anonymous
  • anonymous
You have to solve:\[2x^2+x-2=0\]the formula to solve an equation like:\[ax^2+bx+c=0\rightarrow x=\frac{ -b \pm \sqrt{b^2-4ac} }{ 2a }\]I dont believe you didnt know this formula
anonymous
  • anonymous
in your case a=2, b=1 and c=-2, find the two solutions
anonymous
  • anonymous
I get:x1=0.78 and x2=-1.28 do you ge the same?
anonymous
  • anonymous
you there?
anonymous
  • anonymous
yeah how did you get the .78 and 1.28 when you get left off with \[-1\pm \sqrt{5}\div4\]
anonymous
  • anonymous
so, for you b^2-4ac = 5?
anonymous
  • anonymous
a=2 b=1 c=-2-->b^2-4ac=1-4·2·(-2)=1+16=17
anonymous
  • anonymous
oops i found my mistake , ok I'm with you now
anonymous
  • anonymous
so its \[-1\pm \sqrt{17}\div4\]
anonymous
  • anonymous
Those are the cross points for x-axis
anonymous
  • anonymous
Now find the roots of the denominator. It is straightforward
anonymous
  • anonymous
how do you do that
anonymous
  • anonymous
what are the values of x that make the denomnator =0?
anonymous
  • anonymous
I am sorry, I have to go. To be continued tomorrow, bye
anonymous
  • anonymous
i've figured it out and the asymptotes. can you help me find the x-intercept of x^2-2x+3/x+2

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