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?

   • 9
   • 6
   • does not exist
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?

   • 5
   • does not exist
   • 4
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?

   • 6
   • 12
   • does not exist
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
   • 3
   • 1
5. 5.

   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
6. 6.

   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
7. 7.

   A library fine is $0.25 per started day late. C(t) is the cost after t days. Noah checks just before t = 5. In dollars, what is the limit as t → 5⁻?

   $1.25
8. 8.

   f(x) = x² + k for x < 1 and f(x) = 4x + 2 for x ≥ 1. Ren picks k so the limit at x = 1 exists. What is k?

   5
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