Limits from graphs and tables

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Ari checks the graph shown from both sides of x = 2. What is the limit of f(x) as x → 2?

   • does not exist
   • 4
   • 1
2. 2.

   Bo checks the graph shown from both sides of x = 1. What is the limit of f(x) as x → 1?

   • 4
   • 6
   • does not exist
3. 3.

   Esme checks the graph shown from both sides of x = -2. What is the limit of f(x) as x → -2?

   • does not exist
   • 2
   • -1
4. 4.

   Jun checks the graph shown from both sides of x = 4. What is the limit of f(x) as x → 4?

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

   A tank's depth is d(t) = 2t + 1 for t < 3 and -t + 12 for t ≥ 3. Kira looks near t = 3. What is the limit as t → 3⁻?

   7
6. 6.

   A cart's position is s(t) = 3t + 1 for t ≥ 2 and 4t − 3 for t < 2. Luz looks near t = 2. What is the limit as t → 2⁺?

   7
7. 7.

   A slime batch weighs m(t) = 20 − 2t for t < 5 and 3t − 9 for t ≥ 5. Milo looks near t = 5. What is the limit as t → 5⁻?

   10
8. 8.

   x = 1.99 gives 11.9401; x = 1.999 gives 11.994001; x = 2.001 gives 12.006001; x = 2.01 gives 12.0601. Ren makes the table shown for f(x) = (x³ − 8)/(x − 2), which has no value at x = 2. What is the limit of f(x) as x → 2?

   12
9. 9.

   x = -3.01 gives -6.01; x = -3.001 gives -6.001; x = -2.999 gives -5.999; x = -2.99 gives -5.99. Tala makes the table shown for f(x) = (x² − 9)/(x + 3), which has no value at x = -3. What is the limit of f(x) as x → -3?

   -6
10. 10.

    x = 1.99 gives 4.99; x = 1.999 gives 4.999; x = 2.001 gives 5.001; x = 2.01 gives 5.01. Zee makes the table shown for f(x) = (x² + x − 6)/(x − 2), which has no value at x = 2. What is the limit of f(x) as x → 2?

    5