D(x)=(x^2-12x+20)/(3x) need to be identify in asymptotes, removable discontinuities, and intercepts for the graph of each function.

Answers:

Vertical asymptote: x = 0

Horizontal asymptote: None

Slant asymptote: (1/3)x - 4

Explanation:

d(x) =

      =

Discontinuities: (terms that cancel out from numerator and denominator):

Nothing cancels so there are NO discontinuities.

Vertical asymptote (denominator cannot equal zero):

3x ≠ 0  

÷3   ÷3

x ≠ 0

So asymptote is to be drawn at x = 0

Horizontal asymptote (evaluate degree of numerator and denominator):

degree of numerator (2) > degree of denominator (1)

so there is NO horizontal asymptote but slant (oblique) must be calculated.

Slant (Oblique) Asymptote (divide numerator by denominator):

So, slant asymptote is to be drawn at (1/3)x - 4

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step-by-step explanation: