anonymous
  • anonymous
Graph f(x)=x^2-3x-10/x-2. Find the domain, range, VA, HA/SA
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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misty1212
  • misty1212
HI!!
anonymous
  • anonymous
Hey:)
misty1212
  • misty1212
is it \[\frac{x^2-3x-10}{x-2}\]

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More answers

anonymous
  • anonymous
Yes
misty1212
  • misty1212
ok lets do them one at a time
misty1212
  • misty1212
domain is easy enough, set the denominator equal to zero and solve then say "all real numbers except that one"
misty1212
  • misty1212
what do you get for that? (you can do it in your head)
anonymous
  • anonymous
2
misty1212
  • misty1212
yeah so all numbers except 2
misty1212
  • misty1212
now before we continue, lets make sure this is not a trick question can you factor the numerator and cancel?
anonymous
  • anonymous
Let me see...
misty1212
  • misty1212
hmmi think it does factor, but not cancel !
anonymous
  • anonymous
(x-5)(x+2)/x-2
misty1212
  • misty1212
yeah but nothing cancels, so lets continue but you should always check that first
misty1212
  • misty1212
once we have the domain, we also have the vertical asymptote too
misty1212
  • misty1212
clear or no?
anonymous
  • anonymous
So it is also 2
anonymous
  • anonymous
yes!
misty1212
  • misty1212
careful here
misty1212
  • misty1212
the vertical asymptote is a vertical line, not a number
misty1212
  • misty1212
so you want to return and answer of \(x=2\) the vertical line, not just the number 2
misty1212
  • misty1212
clear?
anonymous
  • anonymous
Oh! Yes! Clear
misty1212
  • misty1212
now for the horizontal asympote the degree of the numerator is ?
anonymous
  • anonymous
2
misty1212
  • misty1212
and the denominator?
anonymous
  • anonymous
there is no horizontal then since it's greater than the denom.
misty1212
  • misty1212
bingo
misty1212
  • misty1212
but the degree of the numerator is one more than the degree of the denominator that means there will be a slant asymptote do you know how to find it?
anonymous
  • anonymous
I never learned about a slant asymptote so I dont know :(
misty1212
  • misty1212
ok it is easy to say what to do , but not easy for me to write in one word "divide"
misty1212
  • misty1212
when you divide a polynomial of degree 2 by a polynomial of degree 1 you get a polynomial of degree 1 ( a line) and a remainder ignore the remainder, the line is the slant asymptote
misty1212
  • misty1212
you can use either long division or (much easier) synthetic division do you know how to do that?
anonymous
  • anonymous
Yes :)
misty1212
  • misty1212
whew like i said it is very hard for me to write division here what do you get?
misty1212
  • misty1212
take your time
anonymous
  • anonymous
I did it in a rush so I got x^2-1x-6.
misty1212
  • misty1212
hmm no you should have a polynomial of degree 1, not a quadratic
misty1212
  • misty1212
1 -3 -10 2 ______________ 1
misty1212
  • misty1212
that is the iniital set up then 1 -3 -10 2 2 ______________ 1 -1
misty1212
  • misty1212
the next line is unimportant since we only need the line, not the remainder the line has the coefficients from the final row so \(x-1\) slant asymptote is \(y=x-1\)
anonymous
  • anonymous
Oh! Now I know what I did wrong! When did the fak divison, i fogot to add the "0^2" Lol but yes, I know understand
misty1212
  • misty1212
ok then we are done!
misty1212
  • misty1212
oh except for the range
anonymous
  • anonymous
I'm so bad at finding that.
misty1212
  • misty1212
in this case it is real easy, since it has a vertical asympote and no horizontal asymptote that means it goes from \(-\infty\) to \(\infty\)
misty1212
  • misty1212
you can write your answer as an interval \((-\infty, \infty)\) or just say "all real numbers"
misty1212
  • misty1212
it is harder for some other ones, but not for this one
anonymous
  • anonymous
Yay! Thanks so much:)))
misty1212
  • misty1212
\[\color\magenta\heartsuit\]

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