Is it continuous? Reading graphs

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   Left-hand limit 4; right-hand limit 4; f(2) not defined. Ari runs the three-part test at x = 2 with the table shown. Which statement is true?

   • f(2) is not defined
   • the limit is not f(2)
   • f is continuous at 2
   • the limit does not exist
2. 2.

   Left-hand limit 2; right-hand limit 5; f(1) = 2. Bo runs the three-part test at x = 1 with the table shown. Which statement is true?

   • f(1) is not defined
   • the limit is not f(1)
   • the limit does not exist
   • f is continuous at 1
3. 3.

   Left-hand limit 3; right-hand limit 3; f(-3) = 1. Esme runs the three-part test at x = -3 with the table shown. Which statement is true?

   • the limit is not f(-3)
   • the limit does not exist
   • f is continuous at -3
   • f(-3) is not defined
4. 4.

   Left-hand limit 6; right-hand limit 6; f(4) = 6. Jun runs the three-part test at x = 4 with the table shown. Which statement is true?

   • f is continuous at 4
   • f(4) is not defined
   • the limit is not f(4)
   • the limit does not exist
5. 5.

   Kira studies f(x) = (x + 3)/(x² − 4). Separated by commas, at which x-values is f not continuous?

   -2, 2
6. 6.

   Luz studies f(x) = (x − 1)/(x² − 9). Separated by commas, at which x-values is f not continuous?

   -3, 3
7. 7.

   Noah studies f(x) = (2x)/(x² − 16). Separated by commas, at which x-values is f not continuous?

   -4, 4
8. 8.

   Pia knows roots, logs and rational functions are continuous on their domains. Where is f(x) = √(x − 2) continuous?

   • x > 2
   • all real numbers
   • x ≥ 2
9. 9.

   Tala knows roots, logs and rational functions are continuous on their domains. Where is f(x) = √(5 − x) continuous?

   • x < 5
   • all real numbers
   • x ≤ 5
10. 10.

    Zee knows roots, logs and rational functions are continuous on their domains. Where is f(x) = 1/√(x − 1) continuous?

    • all real numbers
    • x > 1
    • x ≥ 1