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Worked solution

Check vertical asymptotes of four rational curves

Find the equation(s) of the vertical asymptote(s) for the following curves.

(a) y=1/(3−x)y=1/(3-x).

(b) y=(2x+1)/(x−2)y=(2x+1)/(x-2).

(c) y=x2/(x−1)y=x^2/(x-1).

(d) y=(x2+2x−3)/(x+2)y=(x^2+2x-3)/(x+2).

CJC · Lecture · Self-Practice 2

(a) Check the denominator and numerator

The printed answer is x=3x=3. Independently numerator 11 is nonzero there; 1/(3−x)1/(3-x) is unbounded near 33.

How did this part go?

(b) Check the denominator and numerator

The printed answer is x=2x=2. Independently numerator 2(2)+1=5≠02(2)+1=5\ne0.

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(c) Check the denominator and numerator

The printed answer is x=1x=1. Independently numerator 12=1≠01^2=1\ne0.

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(d) Check the denominator and numerator

The printed answer is x=−2x=-2. Independently numerator (−2)2+2(−2)−3=−3≠0(-2)^2+2(-2)-3=-3\ne0.

How did this part go?

Common mistakes

Check for cancellation before declaring a zero denominator to be an asymptote.

Solution notes

Both original copies visually compared. Independent checks and qualifications are identified in the working. No printed marks or external attribution.

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