SOLUTION: I have to solve this problem for school. Please help Graph this rational function: T(w)= w^2+2w+4/w-1

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Question 690021: I have to solve this problem for school. Please help
Graph this rational function:
T(w)= w^2+2w+4/w-1
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
w-1 = 0

w = 1

So the vertical asymptote is w = 1

Plug in w = 0 to get (w^2+2w+4)/(w-1) = ((0)^2+2(0)+4)/(0-1) = -4.

So the y-intercept is (0,-4)

Since the discriminant of w^2+2w+4 is negative, there are no real solutions, which means that there are no x-intercepts.

Use polynomial long division to get the quotient w+3. So the oblique asymptote is y = x+3

So what we have is this




Note: The blue vertical line should be a dashed line since it's the vertical asymptote. The blue diagonal line should be a dashed line since it's the oblique asymptote.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Graph this rational function:
T(w)= w^2+2w+4/w-1
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You can always plot points.
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Notice that there is a vertical asymptote at w = 1.
Notice that there is no horizontal asymptote because
y = w^2/(0*w^2) is undefined.
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Notice that the "T" intercept is (0,-4)
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graph%28400%2C400%2C-10%2C10%2C-20%2C20%2C%28x%5E2%2B2x%2B4%29%2F%28x-1%29%29
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Cheers,
Stan H.
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