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

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. Read this first

   Table of f

   x	f(x)
   0	1
   1	2
   2	4
   3	8
   4	16
   5	32

2. 1.

   Tala's worksheet shows the table of f. What is the average rate of change of f from x = 1 to x = 4?

   14/3
3. 2.

   In a notebook, Zee has the table of f. What is the average rate of change from x = 1 to x = 5?

   7
4. 3.

   Ari uses the table of f in pencil. How fast does f change, on average, from x = 1 to x = 3?

   12
5. 4.

   On a puzzle card, Bo sees the table of f. What is the average rate of change from x = -3 to x = -1?

   4
6. 5.

   Esme's worksheet shows the graph of f. What is its domain in interval notation?

   • (-∞, ∞)
   • [-2, 4)
   • [1, 7)
   • (-2, 4]
7. 6.

   In a notebook, Jun copies the graph of f shown. Which interval is its range?

   • [-2, 6)
   • (-5, 3]
   • (-∞, ∞)
   • (-2, 6]
8. 7.

   Kira reads the graph of f in pencil. What is the domain of f, in interval notation?

   • [0, 6]
   • (0, 6)
   • (-∞, ∞)
   • [-3, 0]
9. 8.

   On a puzzle card, Luz sees the graph of f. Which interval is the range of f?

   • (-4, 2]
   • (-1, 8]
   • (-∞, ∞)
   • [-1, 8)

10. Table of f

    x	f(x)
    -3	-5
    -2	0
    -1	3
    0	4
    1	3
    2	0
    3	-5

    The graph of f is a smooth curve through these points.

11. 9.

    Milo's worksheet shows the table of f. On which interval is f increasing?

    • (-3, 0)
    • (-5, 4)
    • (0, 3)
    • (-3, 3)
12. 10.

    Pia draws arrows between the rows of the table in pencil. Where is f decreasing?

    • (-1, 2)
    • (2, 5)
    • (-1, 5)
    • (-6, 5)