anonymous
  • anonymous
Graph
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[f(x)= \frac{ x^{2}+x-2 }{ x ^{2-}3x-4 }\]
karatechopper
  • karatechopper
Lets factor!
karatechopper
  • karatechopper
Do you know how to factor?

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More answers

anonymous
  • anonymous
Yes \[\frac{ (x+1)(x-2) }{ (x+1)(x-4) }\]
karatechopper
  • karatechopper
Cool! Okay now, cross out the common factors and what are you left with?
anonymous
  • anonymous
\[\frac{ (x-2) }{ (x-4) }\]
karatechopper
  • karatechopper
Right, okay. Now do you have the slightest idea of what we do now?
anonymous
  • anonymous
Not really haha
karatechopper
  • karatechopper
Alright haha. Well the most simple way of going about this problem is to make an X,Y chart. Just some numbers for your x value, plug into the equation, pop out a Y value. - fill that into the chart. Once you get a few good points, plot. You are set!
karatechopper
  • karatechopper
Would you like me to help you make a X,Y chart?
anonymous
  • anonymous
Yes please
anonymous
  • anonymous
@karatechopper
karatechopper
  • karatechopper
Alright. Let's start.
anonymous
  • anonymous
Thank you :D
karatechopper
  • karatechopper
|dw:1434953607858:dw| Pick 5 x-values for me. Keep them a good range. :)
anonymous
  • anonymous
-2,-1,0,1,2
anonymous
  • anonymous
Isn't that what people usually do
karatechopper
  • karatechopper
|dw:1434953723896:dw| Now, go through each X value and plug each of them into the above equation we simplified to: (x-2)/(x-4), to find each y-value. I will check them after you finish.
karatechopper
  • karatechopper
Also yes, those are common points, sometimes people pick different points because they know what the shape of the graph will look like, but there is not a requirement about which points you pick haha.
anonymous
  • anonymous
\[\frac{ 2 }{ 3 }, -\frac{ 3 }{ 5 }, \frac{ 1 }{ 2 },-\frac{ 1 }{ 3 }, \frac{ 0 }{ -2 }\]
anonymous
  • anonymous
I'm pretty sure some of those are wrong haha
karatechopper
  • karatechopper
Could you show me your work for x-values -1 and 1 please?
campbell_st
  • campbell_st
can I just say... ignore the table of values.... look at the asymptotes the vertical asymptote is when x - 4 = 0 so x = 4 is a vertical asymptote
anonymous
  • anonymous
(-1-2)=-3 (-1-4)=-5
anonymous
  • anonymous
Is that correct?
karatechopper
  • karatechopper
Negatives cancel, leaving you with positive 3/5. Same with x-value you 1, you get a positive 1/3. Also Campbell is right.
campbell_st
  • campbell_st
then the numerator and denominator are both degree 1 polynomials so the horizontal asymptote is at y = x/x or y = 1 not look at the numerator to see the where the cruve cuts the x-axis x - 2 = 0 so the x-intercept is x = 2 lastly the y- intercept let x = 0 and you get y = 1/2 so the graph|dw:1434954017902:dw|
anonymous
  • anonymous
Its two separate lines?
campbell_st
  • campbell_st
a table of values is a waste of time... you need to recognise the curve is a hyperbola... find asymptotes and intercepts then sketch the curve
campbell_st
  • campbell_st
there are 2 parts to the curve
campbell_st
  • campbell_st
and there would be a point of discontinuity at x = -1... in my humble opinion
UsukiDoll
  • UsukiDoll
asymptotes is a calculus topic though... what if the original poster is in an elementary algebra course? Then a chart / table of values is needed.
anonymous
  • anonymous
pre cal
campbell_st
  • campbell_st
but Uki will probably clean up my solution and meake it more readable
UsukiDoll
  • UsukiDoll
ah...so.. ihateschool18 is getting there to asymptotes..
UsukiDoll
  • UsukiDoll
ha ha I need to eat dinner... no seriously...can't do math without food
karatechopper
  • karatechopper
Asymptotes is an Algebra 2 Subject for me. But that's interesting to see how its in Pre-calc too. I remember it being recovered there too.
campbell_st
  • campbell_st
the great is complex... and would need a very large table to get an idea of the whole graph
UsukiDoll
  • UsukiDoll
@karatechopper wow that's early...I was first exposed to it in Calculus I O_O
karatechopper
  • karatechopper
I need sleep. Lol yeah Campbell I thought a table of value would get some of the point across as to how such points can't cross a certain line lol.
campbell_st
  • campbell_st
and I tend to use quick and dirty methods rather than the long and boring ones
anonymous
  • anonymous
Thank you guys so much btw
karatechopper
  • karatechopper
Oye, old school is cool sometimes when getting the point across. xD
karatechopper
  • karatechopper
Welp, I tried haha. Have a good day guys.
karatechopper
  • karatechopper
:)
anonymous
  • anonymous
Thanks and you too
campbell_st
  • campbell_st
the method is sound... just tedious... and in a question of this type.. I would expect the asker has some knowledge of asymptotes
karatechopper
  • karatechopper
Also @UsukiDoll I'm surprised as to how that's popping up in Calculus. Asymptotes appeared in Conics, which absolutely blew my mind to pieces. Conics was not much of a fun subject with all that memorization.

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