How do you find the Vertical, Horizontal, and Oblique Asymptote given $f (x) = \frac{3 x + 5}{x - 2}$ $f(x)= (3x + 5) /( x - 2)$ ?

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Answer 1 · 2016-11-11T11:29:24

The vertical asymptote is $x = 2$ $x=2$
There is no oblique asymptote.
The horizontal asymptoteis $y = 3$ $y=3$

As you cannot divide by $0$ $0$ , the vertical asymptote is $x = 2$ $x=2$

The degree of the numerator is $=$ $=$ to the degree of the denominator, there is no oblique asymptote.

$lim_(x->+-oo)f(x)=3x/x=3$

Therefore $y=3$ is a horizontal asymptote
graph{(y-(3x+5)/(x-2))(y-3)=0 [-25.65, 25.65, -12.83, 12.84]}

How do you find the Vertical, Horizontal, and Oblique Asymptote given f(x)= (3x + 5) /( x - 2)f(x)=3x+5x−2f(x)= (3x + 5) /( x - 2)?