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Question 1029261: I have no idea what this is but the question that I have to solve is "Find the domain, points of discontinuity, x-y- intercepts of each rational function. Determine whether the discontinuities are removable or non-removable." Can you please help me with one so I get an idea of what to do?
Number 1
y= x+5/x^2+9x+20
Found 2 solutions by stanbon, rothauserc:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the domain, points of discontinuity, x-y- intercepts of each rational function. Determine whether the discontinuities are removable or non-removable." Can you please help me with one so I get an idea of what to do?
Number 1
y= x+5/x^2+9x+20 = (x+5)/[(x+4)(x+5)]
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Domain:: All Real Numbers except x = -4 and x = -5
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Note: Since (x+5) is in numerator and denominator, there is a "hole" at x = -5
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x = -5 is a removable discontinuity.
x = 4 is not removable: there is a vertical asymptote at x = -4
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x- intercept ?
Let y = 0 and solve for "x"
No solution, so no x-intercept.
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y- intercept ?
Let x = 0, then y = 5/20 = 1/4
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Graph::
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Cheers,
Stan H.
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! look at the denominator, what value/s of x make the denominator = 0 (points of discontinuity)
:
x^2 +9x +20 = 0
:
(x+5) * (x+4) = 0
:
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points of discontinuity are x = -5 and x = -4
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:
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domain is all real values of x except for -5 and -4
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:
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if x = 0, then y = 1/4 (y intercept)
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:
y = (x+5) / ( (x+5)*(x+4) ) = 1 / (x+4)
:
x+4 = 1/y
:
x = 1/y -4
:
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no x intercepts since y can not be = 0
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:
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the discontinuity x = -5 can be removed but x = -4 cannot be removed
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:
note that we remove x = -5 by refining the function
y = (x+5) / ( (x+5)*(x+4) ) = 1 / (x+4)
:
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