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
   • 1
   • 4
2. 2.

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

   • does not exist
   • 4
   • 6
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
   • -1
   • 2
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 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
6. 6.

   A kite's height is h(t) = 0.5t + 6 for t ≥ 4 and 3t + 2 for t < 4. Noah looks near t = 4. What is the limit as t → 4⁺?

   8
7. 7.

   x = 3.99 gives 7.99; x = 3.999 gives 7.999; x = 4.001 gives 8.001; x = 4.01 gives 8.01. Pia makes the table shown for f(x) = (x² − 16)/(x − 4), which has no value at x = 4. What is the limit of f(x) as x → 4?

   8
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