Limits from graphs and tables

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   f has left limit 2 and right limit 5; g has left limit 4 and right limit 1. Both f and g jump at x = 2, as the table shows. Ari combines them. What is the limit of f + g as x → 2?

   • does not exist
   • 9
   • 6
2. 2.

   f has left limit 1 and right limit 3; g has left limit 2 and right limit 2. Both f and g jump at x = 2, as the table shows. Bo combines them. What is the limit of f + g as x → 2?

   • 4
   • does not exist
   • 5
3. 3.

   f has left limit 2 and right limit 4; g has left limit 3 and right limit 1.5. Both f and g jump at x = 2, as the table shows. Esme combines them. What is the limit of f × g as x → 2?

   • does not exist
   • 6
   • 12
4. 4.

   f has left limit 6 and right limit 2; g has left limit 1 and right limit 1. Both f and g jump at x = 2, as the table shows. Jun combines them. What is the limit of f − g as x → 2?

   • does not exist
   • 1
   • 3
5. 5.

   A bike rental charges $3 for each started hour. C(t) is the cost after t hours. Kira checks just before t = 2. In dollars, what is the limit as t → 2⁻?

   6
6. 6.

   A locker costs $2 for each started day. C(t) is the cost after t days. Luz checks just before t = 4. In dollars, what is the limit as t → 4⁻?

   8
7. 7.

   A paddle boat costs $2 per started half hour. C(t) is the cost after t half hours. Milo checks just before t = 3. In dollars, what is the limit as t → 3⁻?

   6
8. 8.

   f(x) = x² + k for x < 2 and f(x) = 3x + 2 for x ≥ 2. Pia picks k so the limit at x = 2 exists. What is k?

   4
9. 9.

   f(x) = x² + k for x < 3 and f(x) = -1x + 10 for x ≥ 3. Tala picks k so the limit at x = 3 exists. What is k?

   -2
10. 10.

    f(x) = x² + k for x < -3 and f(x) = 2x + 11 for x ≥ -3. Zee picks k so the limit at x = -3 exists. What is k?

    -4