Piecewise continuity and the Intermediate Value Theorem

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   f(x) = kx + 1 for x < 2 and f(x) = x² + 5 for x ≥ 2. Ari picks k so f is continuous at x = 2. What is k?

   4
2. 2.

   f(x) = kx − 2 for x < 3 and f(x) = x² + 1 for x ≥ 3. Bo picks k so f is continuous at x = 3. What is k?

   4
3. 3.

   f(x) = kx + 4 for x < 3 and f(x) = x² + 6 for x ≥ 3. Esme picks k so f is continuous at x = 3. What is k?

   11/3
4. 4.

   f(x) = kx + 5 for x < 2 and f(x) = x² − 1 for x ≥ 2. Jun picks k so f is continuous at x = 2. What is k?

   -1
5. 5.

   A tank holds V(t) = 3t L for t < 2 minutes, then a steady c liters for t ≥ 2. Luz wants no step. What c makes it continuous, in L?

   6
6. 6.

   A cart is at s(t) = 12t m for t < 5 s, then stops at s = c for t ≥ 5. Milo wants no step. What c makes it continuous, in m?

   60
7. 7.

   A slide drops d(x) = 0.25x m for x < 8, then runs flat at depth c for x ≥ 8. Noah wants no step. What c makes it continuous, in m?

   2
8. 8.

   f(0) = -3; f(1) = -2; f(2) = -1; f(3) = 4; f(4) = 6. Ren uses the table shown and the IVT. Where must f have a zero?

   • between 0 and 1
   • between 2 and 3
   • between 3 and 4
9. 9.

   f(0) = 7; f(1) = 5; f(2) = 2; f(3) = 1; f(4) = -2. Tala uses the table shown and the IVT. Where must f have a zero?

   • between 2 and 3
   • between 3 and 4
   • between 1 and 2
10. 10.

    f(0) = -6; f(1) = -4; f(2) = -1; f(3) = 3; f(4) = 4. Zee uses the table shown and the IVT. Where must f have a zero?

    • between 2 and 3
    • between 0 and 1
    • between 1 and 2