Limits that go to infinity at an asymptote

Answer Key - Grade 12 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Ari graphs f(x) = (x + 2)/(x − 3). At what x does f have a vertical asymptote?

   3
2. 2.

   Bo graphs f(x) = (x − 5)/(x + 1). At what x does f have a vertical asymptote?

   -1
3. 3.

   Esme graphs f(x) = (x + 4)/(x − 6). At what x does f have a vertical asymptote?

   6
4. 4.

   Kira traces the graph shown toward the asymptote from the right. What is the limit of f(x) as x → 2⁺?

   • 2
   • −∞
   • ∞
5. 5.

   Luz traces the graph shown toward the asymptote from the left. What is the limit of f(x) as x → -1⁻?

   • ∞
   • -1
   • −∞
6. 6.

   Milo traces the graph shown toward the asymptote from the left. What is the limit of f(x) as x → 3⁻?

   • 3
   • −∞
   • ∞
7. 7.

   Noah traces the graph shown toward the asymptote from the right. What is the limit of f(x) as x → 0⁺?

   • 0
   • ∞
   • −∞
8. 8.

   Pia tests f(x) = 3/(x − 2) just right of the asymptote, at x = 2.01. What is f(2.01)?

   300
9. 9.

   Ren tests f(x) = 5/(x + 1) just left of the asymptote, at x = -1.01. What is f(-1.01)?

   -500
10. 10.

    Zee tests f(x) = -4/(x − 1) just left of the asymptote, at x = 0.99. What is f(0.99)?

    400