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Curve Sketching

You don't need a calculator or computer to draw your graphs! Derivatives and other Calculus techniques give direct insights into the geometric behavior of curves.

Vertical Asymptotes

Evaluate $$\displaystyle{\lim_{x \to 1^+} \left (\frac{2}{ x^2 - 1 }+2 \right ) }.$$

What are the vertical asymptotes of $y = 3 + \frac{6x}{x^2-25} ?$

What is the number of vertical asymptotes of $y = \frac{5x^2}{x^2-9} + 4 ?$

Find the sum of the $$y$$-coordinates of all the distinct intersection points between $$y=x+1$$ and the vertical asymptotes of the curve: $y=\frac{x+5}{x^3-10x^2+33x-36}.$

What is the number of vertical asymptotes of $y = \frac{5x^2}{x^2-25} + 5 ?$

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