unicwaan
  • unicwaan
I need to find the domain and range, x and y intercepts, horizontal and vertical asymptotes. Can someone help me through it please?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
Hi what is your function?
unicwaan
  • unicwaan
There should be a picture attached but it's: X^2 + x - 2 divided by x^2 - 3x - 4
anonymous
  • anonymous
first thing, you should factor the num and denom of your function\[f(x)=\frac{x^2+x-2}{x^2-3x-4}\]have you tried to do so?

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unicwaan
  • unicwaan
I did, the numerator factors into (x-1)(x+2) and the deniminator factors into (x-4)(x+1)
anonymous
  • anonymous
very good, so what will be the domain considering the denom?
unicwaan
  • unicwaan
The domain would be all reals except x=4 and x=-1?
anonymous
  • anonymous
quite right
anonymous
  • anonymous
let's work on range of the function
unicwaan
  • unicwaan
alright
unicwaan
  • unicwaan
Is the range all reals?
anonymous
  • anonymous
thats right, do you have a reasoning for that?
unicwaan
  • unicwaan
Well by the graph it extends infinitely up and down
unicwaan
  • unicwaan
and because quadratic functions' range will always be all reals
anonymous
  • anonymous
that's right, but what if we don't know about the graph
anonymous
  • anonymous
note that quadratics don't cover all reals|dw:1434182772266:dw|
unicwaan
  • unicwaan
Oh okay, then I do not a reasoning
unicwaan
  • unicwaan
do not have a reasoning*
anonymous
  • anonymous
function is continuous on the interval (-1,4) and\[\lim_{x \to -1^{+}} f(x)=\infty \]\[\lim_{x \to 4^{-}} f(x)=-\infty \]therefore range is all of real numbers
anonymous
  • anonymous
does that make sense?
unicwaan
  • unicwaan
So when you plugged in the ordered pair, the output was infinite basically?
anonymous
  • anonymous
thats right
unicwaan
  • unicwaan
okay that makes sense
anonymous
  • anonymous
for example\[\lim_{x \to -1^{+}} f(x)=\frac{1 \times -2}{-5 \times 0^{+}}=\infty\]
anonymous
  • anonymous
ok what are x and y intercepts?
unicwaan
  • unicwaan
Alright so the y intercept = 1/2 because you plug in 0 for x to find y. The x intercept = -2,1 because they are the zeros of the numerator
anonymous
  • anonymous
very right, thanks
anonymous
  • anonymous
and what about asymptotes
unicwaan
  • unicwaan
The horizontal asymptotes is 1 because the degree of each function are the same and therefore, must divide the leading coeeficients. The vertical asymptotes are y= -1,4 because they are the zeros of the denominator.
anonymous
  • anonymous
right, you can put your words in mathematical phrases
anonymous
  • anonymous
now you can graph your function
unicwaan
  • unicwaan
Okay so for the asympotes I put dotted lines to represent them, and then I plugged in points according to get this graph|dw:1434183896630:dw| Poor drawing but the basic jist of it :/
anonymous
  • anonymous
we're done
unicwaan
  • unicwaan
Great! Thank you so much this really helped! :D
anonymous
  • anonymous
no problem

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