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unicwaan
 one year ago
I need to find the domain and range, x and y intercepts, horizontal and vertical asymptotes. Can someone help me through it please?
unicwaan
 one year ago
I need to find the domain and range, x and y intercepts, horizontal and vertical asymptotes. Can someone help me through it please?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Hi what is your function?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1There should be a picture attached but it's: X^2 + x  2 divided by x^2  3x  4

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0first thing, you should factor the num and denom of your function\[f(x)=\frac{x^2+x2}{x^23x4}\]have you tried to do so?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1I did, the numerator factors into (x1)(x+2) and the deniminator factors into (x4)(x+1)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0very good, so what will be the domain considering the denom?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1The domain would be all reals except x=4 and x=1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0let's work on range of the function

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Is the range all reals?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats right, do you have a reasoning for that?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Well by the graph it extends infinitely up and down

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1and because quadratic functions' range will always be all reals

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that's right, but what if we don't know about the graph

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0note that quadratics don't cover all realsdw:1434182772266:dw

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Oh okay, then I do not a reasoning

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1do not have a reasoning*

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0function 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
 one year ago
Best ResponseYou've already chosen the best response.0does that make sense?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1So when you plugged in the ordered pair, the output was infinite basically?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1okay that makes sense

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for example\[\lim_{x \to 1^{+}} f(x)=\frac{1 \times 2}{5 \times 0^{+}}=\infty\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok what are x and y intercepts?

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Alright 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
 one year ago
Best ResponseYou've already chosen the best response.0and what about asymptotes

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1The 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
 one year ago
Best ResponseYou've already chosen the best response.0right, you can put your words in mathematical phrases

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now you can graph your function

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Okay so for the asympotes I put dotted lines to represent them, and then I plugged in points according to get this graphdw:1434183896630:dw Poor drawing but the basic jist of it :/

unicwaan
 one year ago
Best ResponseYou've already chosen the best response.1Great! Thank you so much this really helped! :D
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