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)
   -1	0
   0	0
   1	2
   2	6
   3	12
   4	20
   5	30

2. 1.

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

   7
3. 2.

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

   12
4. 3.

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

   4
5. 4.

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

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

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

   • (0, 6)
   • [-3, 0]
   • [0, 6]
   • (-∞, ∞)
7. 6.

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

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

8. 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.

9. 7.

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

   • (-3, 3)
   • (-5, 4)
   • (-3, 0)
   • (0, 3)
10. 8.

    In a notebook, Noah reads the table of f row by row. On which interval is f increasing?

    • (-2, 1)
    • (1, 4)
    • (-2, 4)
    • (-2, 7)
11. 9.

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

    • (2, 5)
    • (-1, 5)
    • (-1, 2)
    • (-6, 5)
12. 10.

    On a puzzle card, Ren sees the table of f. On which interval is f decreasing?

    • (-4, -1)
    • (0, 9)
    • (-4, 2)
    • (-1, 2)