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 18 (where x is 3)
   • The value -18 (where x is -3)
   • The value 2 (where x is -1)
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 16 (where x is 4)
   • The value -20 (where x is -2)
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 22 (where x is -2)
   • The value 2 (where x is 0)
   • The value 6 (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 = -2 and x = 3
   • x = -1 and x = 2
   • x = -1 only
   • x = 1 and x = 4

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

   0 | 1; 1 | 2; 2 | 4; 3 | 8; 4 | 16; 5 | 32. Table of g (x | g(x)): 0 | 1; 1 | 2; 2 | 3; 3 | 4; 4 | 5; 5 | 6.

8. 6.

   In a notebook, Luz compares the tables of f(x) = 2ˣ and g(x) = x + 1. Where does f(x) = g(x)?

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

9. 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.

10. 7.

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

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.

    Tala works in pencil: f is the table and g(x) = 2x. From x = 0 to x = 16, by how much do the average rates differ?

    7/4