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.

   In a notebook, Zee has f(x) = 3ˣ. What is its average rate of change from x = 0 to x = 2?

   4
3. 3.

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

   7
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) → -∞
   • f(x) → ∞
   • f(x) → 0
5. 5.

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

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

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

   • f(x) → -∞
   • f(x) → 0
   • f(x) → ∞
   • f(x) → 2
7. 7.

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

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

   In a notebook, Noah studies f(x) = -x³ + 5. As x → -∞, where does f(x) go?

   • f(x) → 0
   • f(x) → ∞
   • f(x) → -∞
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 = 1
   • x = -2 and y = 1
   • x = 1 and y = 2
   • x = 2 and y = 3
10. 10.

    On a puzzle card, f(x) = 5 · 2ˣ + 4. Zee needs its asymptotes. Which are they?

    • x = 4 only
    • y = 5 only
    • y = 4 only
    • y = 0 only