Question 528628: For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work. f(x) = 4x/7x^2+6x-16 +25
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! For the following function find the vertical, horizontal, and oblique asymptotes, if any. Please show all of your work. f(x) = 4x/7x^2+6x-16 +25
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f(x) = 4x/(7x^2+6x+9)
When the degree of the numerator is less than that of the denominator, as in this case, the horizontal asymptote is the x-axis.
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Vertical Asymptotes occur when x-values make the denominator=0.
In this case, because of the constant 9, the denominator can never be zero.
Therefore, there are no vertical asymptotes.
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Oblique asymptotes occur only if the numerator is one degree higher than that of the denominator; therefore, there are no oblique asymptotes in this case.
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