Excluded values, asymptotes and graphs of rational functions

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Luz graphs f(x) = (x + 1)/(x² − x − 6) on a worksheet. What are the x-values of the vertical asymptotes?

   -2, 3
2. 2.

   Milo graphs f(x) = (x − 2)/(x² + 4x − 5) in a notebook. What are the x-values of the vertical asymptotes?

   -5, 1
3. 3.

   Noah graphs f(x) = (x + 6)/(x² − 9) in pencil. What are the x-values of the vertical asymptotes?

   -3, 3
4. 4.

   Ren graphs f(x) = (x − 2)/(x² + x − 6) on a worksheet. Which describes the graph at the x-values that make the bottom 0?

   • a vertical asymptote x = -3 only
   • vertical asymptotes x = -3 and x = 2
   • a hole at x = -3 and a vertical asymptote x = 2
   • a hole at x = 2 and a vertical asymptote x = -3
5. 5.

   Tala graphs f(x) = (x + 4)/(x² + 3x − 4) in a notebook. Which describes the graph at the x-values that make the bottom 0?

   • vertical asymptotes x = -4 and x = 1
   • a vertical asymptote x = 1 only
   • a hole at x = -4 and a vertical asymptote x = 1
   • a hole at x = 1 and a vertical asymptote x = -4
6. 6.

   Zee graphs f(x) = (x − 5)/(x² − 7x + 10) in pencil. Which describes the graph at the x-values that make the bottom 0?

   • a vertical asymptote x = 2 only
   • a hole at x = 5 and a vertical asymptote x = 2
   • a hole at x = 2 and a vertical asymptote x = 5
   • vertical asymptotes x = 2 and x = 5
7. 7.

   Bo studies f(x) = (6x + 1)/(2x − 5) on a worksheet. What is the horizontal asymptote, y = ?

   3
8. 8.

   Esme studies f(x) = (6x² − 3)/(4x² + 5) in a notebook. What is the horizontal asymptote, y = ?

   3/2
9. 9.

   Jun studies f(x) = (10x + 1)/(2x² − 7) in pencil. What is the horizontal asymptote, y = ?

   0
10. 10.

    Kira studies f(x) = 8x/(2x² + 1) − 1 from a math book. What is the horizontal asymptote, y = ?

    -1