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anonymous
 one year ago
f(x)=2x2x3/x22x3
graph and find the domain,range, and VA
anonymous
 one year ago
f(x)=2x2x3/x22x3 graph and find the domain,range, and VA

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1439337786064:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Do you mean \(\Large f(x)=\frac{2x^2−x−3}{x^2−2x−3}\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Do you know how to factorize quadratic expressions?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So I got for the first one, (x+1)(2x3)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So factor the numerator and denominator, as a start! ok?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Got it:) So, I gottt (x+1)(2x3)/(x+1)(x3)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Yep! Good job! So you have: \(\Large f(x)=\frac{(2x3)(x+1)}{(x3)(x+1)}\) Do you notice anything that could help you?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Canceling out the x+1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Just like that, or with a condition?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont know what you mean by that? So, I'm going w/ "just like that."

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Well, when you cancel factors in a division, you have to make sure that the factor will never become zero. So you can cancel ONLY if you specify x+1\(\ne\)0., in other words, x\(\ne1\).

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So what are you left with?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1or \(\Large f(x)=\frac{(2x3)}{(x3)}, .... x\ne 1\)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1What else do you see?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You can take out the x3 and ur left with the 2

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You cannot simplify further, so you have to think of graphing what's left.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1What graphing features do you see in the simplified function?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It goes in opposite directions

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Well, have you learned about asymptotes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A horizontal asymptote for this may be 2/3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Horizontal asymptote is correct, but not at 3/2. Horizontal asymptote can be obtained by taking limits of f(x) as x>inf and x>inf.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Do you see a vertical asymptote?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no! Okay thats wrong! I mean 3,3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Almost! Vertical asymptotes are governed by the denominator becoming zero, so you need to find x for which (x3)=0, or x=3. That's where the vertical asymptote is located.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439339170261:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1What about the horizontal asymptote?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hm...I give up on that one haha! So, I'm just going to guess and say 2/1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1You would divide the coefficients of x, so 2x/x=2, yes 2/1=2 is correct.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439339327350:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0:) Yay! Now what about the domain and range?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1We'll finish drawing the graph first. Do you know what it looks like?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A point of intersection? Between the vertical and horizontal lines

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1No this graph does not intersect itself, but it runs close to the two asymptotes that i drew.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1To know which quadrant the graph goes, you would evaluate f(x) at a point just to the left of x=3 (say 2.9) and a point just to the right of x=3, say 3.1 and find out where to plot the lines. So can you find f(2.9) and f(3.1)?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1not really, f(2.9)=(2*2.93)/(2.93)=2.8/(0.1)=28 Your turn to do the same for f(3.1)...

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1It's +32. The denominator is +0.1.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1So now we can complete the graph, remembering that \(x\ne1\) !

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1dw:1439339824439:dw

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Can you now do the domain and range?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'll try. So y>1 and the domain could be all real numbers except 3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1How about 1 which we have shown an empty circle?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1We said to cancel the common factor (x+1), we need to put the restriction \(x+1\ne 0\) or \(x\ne 1\), so =1 cannot show up in the domain, right?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1*1 So what is the domain?

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Your proposed domain was almost right, except that you missed out the 1, so...

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Ok:) Thanks<3 I thought so, but I wasnt sure

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0all reals except 3,1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Good! Now proceed with the range, and you'd be done!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0**Silence** Takes a wild guess and goes with...y>2/3

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1Look at the graph for a start! There are two points to be excluded.

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1We're looking at range, or the yaxis. So look for yvalues that we cannot get from the graph!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0On the graph? ok so 1

mathmate
 one year ago
Best ResponseYou've already chosen the best response.11 is for x. What is the corresponding value for y????

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I.e. what is f(x) as x > 1?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i gotta go eat dinner! Thanks so much for all your help:). I'll be back in 30 minutes or so:)

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1I will be gone by then. Someone else should be able to continue! Bon apetite!
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