Excluded values, asymptotes and graphs of rational functions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Milo graphs f(x) = (x² − 3x − 10)/(x² + x − 2) in a notebook. What point is the hole?

   (-2, 7/3)
2. 2.

   Noah graphs f(x) = (x² − 6x + 8)/(x² − x − 12) in pencil. What point is the hole?

   (4, 2/7)
3. 3.

   Pia graphs f(x) = (x² + 7x + 6)/(x² − x − 2) from a math book. What point is the hole?

   (-1, -5/3)
4. 4.

   Ren graphs f(x) = (x² − 9)/(x² − 4x + 3) on a worksheet. At which x-values does the graph cross the x-axis?

   -3
5. 5.

   Tala graphs f(x) = (x² − 4)/(x² + 5x + 6) in a notebook. At which x-values does the graph cross the x-axis?

   2
6. 6.

   Zee graphs f(x) = (x² + x − 20)/(x² − 16) in pencil. At which x-values does the graph cross the x-axis?

   -5
7. 7.

   Bo writes the domain of f(x) = (x + 2)/(x² − 3x − 10) on a worksheet. Which is the domain in interval notation?

   • (-∞, -5) ∪ (-5, 2) ∪ (2, ∞)
   • (-∞, ∞)
   • (-∞, -2) ∪ (-2, 5) ∪ (5, ∞)
   • (-∞, 5) ∪ (5, ∞)
8. 8.

   Esme writes the domain of f(x) = (x − 1)/(x² + 5x − 6) in a notebook. Which is the domain in interval notation?

   • (-∞, -1) ∪ (-1, 6) ∪ (6, ∞)
   • (-∞, -6) ∪ (-6, ∞)
   • (-∞, ∞)
   • (-∞, -6) ∪ (-6, 1) ∪ (1, ∞)
9. 9.

   Jun writes the domain of f(x) = (x + 5)/(x² + 3x − 10) in pencil. Which is the domain in interval notation?

   • (-∞, -2) ∪ (-2, 5) ∪ (5, ∞)
   • (-∞, 2) ∪ (2, ∞)
   • (-∞, ∞)
   • (-∞, -5) ∪ (-5, 2) ∪ (2, ∞)
10. 10.

    Kira writes the domain of f(x) = (x − 4)/(x² − 2x − 8) from a math book. Which is the domain in interval notation?

    • (-∞, -4) ∪ (-4, 2) ∪ (2, ∞)
    • (-∞, -2) ∪ (-2, 4) ∪ (4, ∞)
    • (-∞, -2) ∪ (-2, ∞)
    • (-∞, ∞)