anonymous
  • anonymous
How do I identify the intercepts, removable continuities, and asymptotes? (2x^3-3x+1)/x^3-5x+7
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@ganeshie8
ganeshie8
  • ganeshie8
are you allowed to graph the function ?
anonymous
  • anonymous
nope :/ i think i'm supposed to solve it based on just the equation

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More answers

ganeshie8
  • ganeshie8
Finding horizontal asymptotes is easy for a rational function
ganeshie8
  • ganeshie8
\[y = \dfrac{\color{Red}{2}x^3-3x+1}{\color{red}{1}x^3-5x+7}\] As \(x\) gets large, the lower degree terms don't matter much, so the value approaches \[y \approx \dfrac{\color{Red}{2}x^3}{\color{red}{1}x^3} = \dfrac{\color{Red}{2}}{\color{red}{1}}=\color{red}{2}\] so \(\color{red}{y=2}\) is an horizontal asymptote
anonymous
  • anonymous
thank you!! is the vertical asymptote about 2.75?
anonymous
  • anonymous
x^3-5x=-7 right? and solve for x
ganeshie8
  • ganeshie8
it should be around x= -2.75 but how did u get that ?
ganeshie8
  • ganeshie8
Yes
anonymous
  • anonymous
okay thanks!! i'm super confused on finding the x intercepts though
ganeshie8
  • ganeshie8
did you find y intercepts ?
anonymous
  • anonymous
yeah i got 1/7 by plugging in 0 in place of x
ganeshie8
  • ganeshie8
Good. use the same trick simply plugin y=0 to get the x intercepts
ganeshie8
  • ganeshie8
\[y = \dfrac{\color{black}{2}x^3-3x+1}{\color{black}{1}x^3-5x+7}\] plugin y=0 for x intercepts \[0 = \dfrac{\color{black}{2}x^3-3x+1}{\color{black}{1}x^3-5x+7}\]
ganeshie8
  • ganeshie8
which is same as \[0 =\color{black}{2}x^3-3x+1\] solve
ganeshie8
  • ganeshie8
wolfram gives 3 x intercepts http://www.wolframalpha.com/input/?i=solve+2x%5E3-3x%2B1%3D0
anonymous
  • anonymous
could i use the formula bc of the plus and minus?
anonymous
  • anonymous
quadratic formula*
ganeshie8
  • ganeshie8
nope, the equation is cubic, not quadratic. i would simply use calculator/wolfram
anonymous
  • anonymous
i'm confused on how i would get 3 answers :/
ganeshie8
  • ganeshie8
why ? it is fine to have multiple x intercepts
ganeshie8
  • ganeshie8
that just means, the graph cuts the x axis at 3 different places
anonymous
  • anonymous
i used mathway and it gave me (1,0) and (-1+-sqrt3)/2 but i'm not sure how it got that
ganeshie8
  • ganeshie8
|dw:1437717579760:dw|
anonymous
  • anonymous
oh i see it haha thank you so much :)

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