Rational functions are functions that can be written as a ratio of two polynomials. Graphing them involves finding key features like asymptotes, intercepts, and holes. Asymptotes are lines that the graph approaches but doesn't cross (vertical and horizontal), and intercepts are points where the graph crosses the x and y axes. Finding these features helps you sketch an accurate representation of the function.
This worksheet focuses on identifying these key features and using them to create accurate graphs. Remember to simplify the rational function first to identify any holes!
Match the following terms with their definitions:
| Term | Definition |
|---|---|
| 1. Vertical Asymptote | A. A point where the function is undefined due to a factor canceling out. |
| 2. Horizontal Asymptote | B. A line that the graph approaches as x approaches infinity or negative infinity. |
| 3. X-intercept | C. The value of x where the function equals zero. |
| 4. Y-intercept | D. A line that the graph approaches as x approaches a specific value, where the denominator is zero. |
| 5. Hole | E. The value of y where the function crosses the y-axis. |
Match the correct letters (A-E) with the numbers (1-5).
To graph a rational function, first find the _________ by setting the denominator equal to zero. Then, find the _________ by comparing the degrees of the numerator and denominator. The _________ is found by setting the numerator equal to zero, and the _________ is found by evaluating the function at x=0. Finally, look for any _________ by identifying factors that cancel out.
Explain in your own words how the location of vertical asymptotes and holes relate to the domain of a rational function.
Please log in to post your answer.
Log InEarn 2 Points for answering. If your answer is selected as the best, you'll get +20 Points! 🚀