# Identify all holes, asymptots, x & y intercepts with a sketch: Parobolic asymptote 2x^3-3x^2-8x-3/x-2 = (x+1)(2x^2-5x-3)/x-2 (this is 1 equation)

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Expert Answers

rcmath | Certified Educator

The right hand side of your equation is the factored form of the left hand side. in other words, what you wrote is y=y.

So I assuming that you are asking us to study `y=(2x^3-3x^2-8x-3)/(x-2)`

1) **y-intercepts**

x=0 => `y=(-3)/(-2)=3/2`

**Hence y-int (0,3/2)**

2) **x-intercepts**

y=0 =>`2x^-3x^2-8x-3=0=>(x+1)(2x^2-5x-3)=0=>`

`(x+1)(x-3)(2x+1)=0=> x=-1, or x=3, or x=-1/2`

Hence **x-intercepts are (-1,0), (3,0), (-1/2,0)**

3) **vertical Asymptote**

x=2 makes denominator zero=> horizontal asymptote

**x=2 vertical asym**

4) No oblique asymptote or horizontal

5)Holes are points that sets the numerator and denominator to be zero, we don't have any in our case.

The following graph confirm our findings.