Vertical Asymptotes Worksheet with Answer Key

What's on the worksheet

1. Find every vertical asymptote and what y does approaching it from each side.
   y = \dfrac{x^2 + 1}{6 - 2x}y = \dfrac{x}{x^2 - 2x + 1}y = \dfrac{x - 5}{x^2 - 6x + 9}y = \dfrac{x + 1}{x^2 - x - 6}
2. Decide whether each function has a hole or an asymptote at x equal to 2.
   y = \dfrac{x^2 - 3x + 2}{x^2 - 4}y = \dfrac{x^2 - 3x + 2}{x^2 - 4x + 4}y = \dfrac{x^3 - 8}{x - 2}y = \dfrac{x^2 - 4}{(x - 2)^3}
3. Read the rule of the rational function from the graph with its dashed asymptotes.
4. Write a rational function of least degree with the stated asymptotes and features.
5. Word problem: the pitch heard from a jet flying toward a listener.
6. Decide hole or asymptote at x equal to 3 for different powers on top and bottom.