Limits that go to infinity at an asymptote

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   Bo studies f(x) = (x − 3)/((x − 1)(x + 2)) as x → 1⁻. What is the limit?

   • f(x) → −∞ as x → 1⁻
   • no limit as x → 1⁻
   • f(x) → +∞ as x → 1⁻
2. 2.

   Esme studies f(x) = (x + 4)/((x + 1)(x − 3)) as x → -1⁺. What is the limit?

   • f(x) → +∞ as x → -1⁺
   • no limit as x → -1⁺
   • f(x) → −∞ as x → -1⁺
3. 3.

   f(x) = (x + c)/(x² − 2x − 15) has two vertical asymptotes. Kira picks c to turn the right one into a hole. What is c?

   -5
4. 4.

   f(x) = (x + c)/(x² − 3x − 28) has two vertical asymptotes. Luz picks c to turn the right one into a hole. What is c?

   -7
5. 5.

   f(x) = (x + c)/(x² − 5x − 36) has two vertical asymptotes. Milo picks c to turn the right one into a hole. What is c?

   -9
6. 6.

   f(x) = (x + c)/(x² − 5x − 24) has two vertical asymptotes. Noah picks c to turn the right one into a hole. What is c?

   -8
7. 7.

   A magnifying glass has focal length 10 cm, and its magnification is m(d) = 10/(10 − d) for an object d cm away. Pia checks d → 10⁻. What is the limit?

   • no limit as d → 10⁻
   • m(d) → −∞ as d → 10⁻
   • m(d) → +∞ as d → 10⁻
8. 8.

   The same lens: m(d) = 10/(10 − d), with d the object's distance in cm. Ren checks d → 10⁺. What is the limit?

   • no limit as d → 10⁺
   • m(d) → +∞ as d → 10⁺
   • m(d) → −∞ as d → 10⁺
9. 9.

   A model rocket's tracking camera zooms by z(d) = 6/(d − 6) as the rocket's distance d nears 6 km. Tala checks d → 6⁺. What is the limit?

   • z(d) → −∞ as d → 6⁺
   • no limit as d → 6⁺
   • z(d) → +∞ as d → 6⁺
10. 10.

    The same camera's zoom is z(d) = 6/(d − 6), with d in km. Zee checks d → 6⁻. What is the limit?

    • z(d) → +∞ as d → 6⁻
    • z(d) → −∞ as d → 6⁻
    • no limit as d → 6⁻