Lesson 2: Graphing Rational Functions — Practice Questions

1. 1. What is the equation of the vertical asymptote for the function $y = \frac{4x - 1}{x + 5}$? The equation is $x = $ ___.

2. 2. What is the equation of the horizontal asymptote for the function $y = \frac{6x + 5}{2x - 8}$? The equation is $y = $ ___.

3. 3. Which of the following are the asymptotes for the rational function $y = \frac{3x - 2}{x - 4}$?

   • A. Vertical: $x=4$, Horizontal: $y=3$
   • B. Vertical: $x=-4$, Horizontal: $y=3$
   • C. Vertical: $x=4$, Horizontal: $y=-2$
   • D. Vertical: $x=3$, Horizontal: $y=4$

4. 4. Identify the vertical and horizontal asymptotes for the function $y = \frac{5}{x - 1} + 3$.

   • A. Vertical: $x=1$, Horizontal: $y=3$
   • B. Vertical: $x=-1$, Horizontal: $y=3$
   • C. Vertical: $x=1$, Horizontal: $y=5$
   • D. Vertical: $x=5$, Horizontal: $y=-1$

5. 5. To help graph the function $y = \frac{x + 7}{x - 1}$, we can find the y-intercept. What is the y-coordinate when $x=0$? The y-coordinate is ___.

6. 6. What is the equation of the vertical asymptote of the graph of $y = \frac{5}{x-7} + 2$? The equation is $x = $ ___.

7. 7. What is the equation of the horizontal asymptote of the graph of $y = \frac{-3}{x+5} - 8$? The equation is $y = $ ___.

8. 8. Which of the following are the equations for the asymptotes of the function $y = \frac{4}{x+1} + 6$?

   • A. Vertical: $x = -1$, Horizontal: $y = 6$
   • B. Vertical: $x = 1$, Horizontal: $y = 6$
   • C. Vertical: $x = 6$, Horizontal: $y = -1$
   • D. Vertical: $x = 4$, Horizontal: $y = 6$

9. 9. For the function $y = \frac{a}{x-h} + k$, which parameter affects the steepness of the graph but not the location of the asymptotes?

   • A. a
   • B. h
   • C. k
   • D. x

10. 10. The graph of the function $y = \frac{10}{x} - 3$ has a vertical asymptote. What is the value of $x$ for this asymptote? $x = $ ___.