Excluded values, asymptotes and graphs of rational functions

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   x = -4.1, -4.01, -3.99, -3.9; f(x) = -19, -199, 201, 21. Luz makes a table for f(x) = 2/(x + 4) + 1 on a worksheet. Where is the vertical asymptote, x = ?

   -4
2. 2.

   x = 1.9, 1.99, 2.01, 2.1; f(x) = -35, -305, 295, 25. Milo makes a table for f(x) = 3/(x − 2) − 5 in a notebook. Where is the vertical asymptote, x = ?

   2
3. 3.

   x = 4.9, 4.99, 5.01, 5.1; f(x) = 13, 103, -97, -7. Noah makes a table for f(x) = -1/(x − 5) + 3 in pencil. Where is the vertical asymptote, x = ?

   5
4. 4.

   x = -3.1, -3.01, -2.99, -2.9; f(x) = -41, -401, 399, 39. Pia makes a table for f(x) = 4/(x + 3) − 1 from a math book. Where is the vertical asymptote, x = ?

   -3
5. 5.

   x = 12, 102, 1002; f(x) = 4.3, 4.03, 4.003. Ren makes a table for f(x) = 3/(x − 2) + 4 with big inputs on a worksheet. What is the horizontal asymptote, y = ?

   4
6. 6.

   x = 9, 99, 999; f(x) = 2.8, 2.98, 2.998. Tala makes a table for f(x) = -2/(x + 1) + 3 with big inputs in a notebook. What is the horizontal asymptote, y = ?

   3
7. 7.

   x = 7, 97, 997; f(x) = -1.5, -1.95, -1.995. Zee makes a table for f(x) = 5/(x + 3) − 2 with big inputs in pencil. What is the horizontal asymptote, y = ?

   -2
8. 8.

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

   • (-∞, ∞)
   • (-∞, -2) ∪ (-2, ∞)
   • (-∞, 3) ∪ (3, ∞)
   • (-∞, -3) ∪ (-3, ∞)
9. 9.

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

   • (-∞, 5) ∪ (5, ∞)
   • (-∞, 1) ∪ (1, ∞)
   • (-∞, ∞)
   • (-∞, -1) ∪ (-1, ∞)
10. 10.

    Kira writes the domain of f(x) = (x − 1)/(x − 7) from a math book. Which is the domain?

    • x < 1 or x > 1
    • every real number x
    • x < 7 or x > 7
    • x < -7 or x > -7