Key features of a graph: intervals, extremes, end behavior and asymptotes

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   On a worksheet, f(x) = √x. Tala finds the average rate of change from x = 4 to x = 16. What is it?

   1/6
2. 2.

   Ari works in pencil with f(x) = x³. What is the average rate of change from x = -1 to x = 3?

   7
3. 3.

   On a puzzle card, f(x) = 12/x. Bo needs the average rate of change from x = 1 to x = 4. What is it?

   -3
4. 4.

   On a worksheet, f(x) = -2x³ + x. Esme describes the end of the graph. As x → ∞, what happens to f(x)?

   • f(x) → 0
   • f(x) → -∞
   • f(x) → ∞
5. 5.

   In a notebook, Jun sketches f(x) = x⁴ − 5x². As x → -∞, where do the outputs go?

   • f(x) → -∞
   • f(x) → ∞
   • f(x) → 0
6. 6.

   Kira works in pencil with f(x) = 2ˣ − 3. As x → -∞, what does f(x) do?

   • f(x) → -3
   • f(x) → -∞
   • f(x) → 0
   • f(x) → ∞
7. 7.

   On a puzzle card, f(x) = 1/x + 2. Luz needs the end behavior as x → ∞. Which is it?

   • f(x) → 0
   • f(x) → -∞
   • f(x) → 2
   • f(x) → ∞
8. 8.

   On a worksheet, Milo has f(x) = -x⁴ + 3x. As x → -∞, what happens to f(x)?

   • f(x) → -∞
   • f(x) → ∞
   • f(x) → 0
9. 9.

   On a worksheet, f(x) = 3/(x − 2) + 1. Pia draws its asymptotes as dashed lines. Which are they?

   • x = 2 and y = 3
   • x = -2 and y = 1
   • x = 2 and y = 1
   • x = 1 and y = 2
10. 10.

    In a notebook, Ren sketches f(x) = 2/(x + 4) − 3. What are its asymptotes?

    • x = 4 and y = -3
    • x = -3 and y = -4
    • x = -4 and y = 2
    • x = -4 and y = -3