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

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   The graph of f is a smooth curve through these points, from x = -3 to x = 3 only. On a worksheet, f(x) = x³ − 3x is drawn only for -3 ≤ x ≤ 3. Ari needs the absolute maximum. Which is it?

   • The value 2 (where x is -1)
   • The value 18 (where x is 3)
   • The value -18 (where x is -3)
2. 2.

   The graph of f is a smooth curve through these points, from x = -2 to x = 4 only. In a notebook, Bo has the table of f(x) = x³ − 3x² for -2 ≤ x ≤ 4. What is the absolute minimum there?

   • The value -4 (where x is 2)
   • The value -20 (where x is -2)
   • The value 16 (where x is 4)
3. 3.

   The graph of f is a smooth curve through these points, from x = -4 to x = 5 only. Esme works in pencil with f(x) = -x³ + 12x on -4 ≤ x ≤ 5. Which is the absolute minimum?

   • The value 16 (where x is -4)
   • The value -16 (where x is -2)
   • The value -65 (where x is 5)
4. 4.

   The graph of f is a smooth curve through these points, from x = -2 to x = 3 only. On a puzzle card, f(x) = -x³ + 3x² + 2 is kept to -2 ≤ x ≤ 3. Jun wants the absolute maximum. Which is it?

   • The value 2 (where x is 0)
   • The value 6 (where x is 2)
   • The value 22 (where x is -2)

5. Read this first

   Table of f (x | f(x))

   -2 | 4; -1 | 1; 0 | 0; 1 | 1; 2 | 4; 3 | 9. Table of g (x | g(x)): -2 | 0; -1 | 1; 0 | 2; 1 | 3; 2 | 4; 3 | 5.

6. 5.

   Kira's worksheet has tables for f(x) = x² and g(x) = x + 2. For which x is f(x) = g(x)?

   • x = -1 and x = 2
   • x = 1 and x = 4
   • x = -1 only
   • x = -2 and x = 3

7. Table of f (x | f(x))

   0 | 0; 1 | 1; 4 | 2; 9 | 3; 16 | 4. Table of g (x | g(x)): 0 | 0; 1 | 1/2; 4 | 2; 9 | 9/2; 16 | 8.

8. 6.

   Milo lines up the tables of f(x) = √x and g(x) = x/2 in pencil. For which x is f(x) = g(x)?

   • x = 0 and x = 4
   • x = -1 and x = 5
   • x = 0 only
   • x = 0 and x = 2

9. Table of f (x | f(x))

   -4 | 4; -2 | 2; 0 | 0; 2 | 2; 4 | 4; 6 | 6. Table of g (x | g(x)): -4 | 1; -2 | 2; 0 | 3; 2 | 4; 4 | 5; 6 | 6.

10. 7.

    On a puzzle card, Noah sees tables for f(x) = |x| and g(x) = x/2 + 3. Where is f(x) = g(x)?

    • x = -2 only
    • x = 2 and x = 6
    • x = -3 and x = 7
    • x = -2 and x = 6

11. Table of f

    x	f(x)
    1	10
    2	7
    3	4
    4	1

12. 8.

    Pia's worksheet has a table for f and the rule g(x) = 2ˣ. From x = 1 to x = 4, how much greater is the larger average rate of change?

    23/3
13. 9.

    In a notebook, Ren compares the table of f with g(x) = 5x − 4, from x = 2 to x = 6. By how much is one average rate greater?

    3
14. 10.

    On a puzzle card, f is a table and g(x) = x². Zee compares their average rates from x = -1 to x = 2. How much greater is the larger one?

    4