Radical and rational functions and equations Knowledge-Based Practice

Questions

1. 1.

   What is the equation of the slant (oblique) asymptote of the rational function $f(x) = \frac{3x^2 - 2x + 4}{x + 1}$?

   • A) $y = 3x + 1$
   • B) $y = 3x - 2$
   • C) $y = 3x + 5$
   • D) $y = 3x - 5$
2. 2.

   What are the coordinates of the removable discontinuity (hole) in the graph of the rational function $f(x) = \frac{2x^2 - 5x - 3}{x^2 - 9}$?

   • A) $(-3, 1)$
   • B) $\left(3, \frac{1}{2}\right)$
   • C) $\left(3, \frac{5}{6}\right)$
   • D) $\left(3, \frac{7}{6}\right)$
3. 3.

   What is the domain of the real-valued function $f(x) = \frac{\sqrt{x + 5}}{x^2 - 4}$?

   • A) $(-5, -2) \cup (-2, 2) \cup (2, \infty)$
   • B) $[-5, -2) \cup (-2, 2) \cup (2, \infty)$
   • C) $[-5, \infty)$
   • D) $(-\infty, -2) \cup (-2, 2) \cup (2, \infty)$
4. 4.

   What is the complete set of real solutions to the equation $\frac{2x}{x - 3} - \frac{3}{x + 1} = \frac{12}{x^2 - 2x - 3}$?

   • A) $x = -1$ and $x = \frac{3}{2}$
   • B) $x = -\frac{3}{2}$
   • C) There are no real solutions.
   • D) $x = \frac{3}{2}$
5. 5.

   What is the complete solution set of the equation $\sqrt{2x + 9} - x = -3$?

   • A) $\{0, 8\}$
   • B) $\{8\}$
   • C) $\{0\}$
   • D) $\emptyset$

Answers and step-by-step solutions appear after you finish the test.