PRECAL.MATH.2.K
Analyze characteristics of rational functions and the behavior of the function around the asymptotes, including horizontal, vertical, and oblique asymptotes.
Precalculus · Texas Essential Knowledge and Skills (TEKS) · TEKS 2012
Standard Unwrapping
AI-generated as a starting point — sign in to edit.Vocabulary
characteristicsrational functionsbehaviorfunctionasymptoteshorizontal asymptotesvertical asymptotesoblique asymptotes
Skills
- analyze (characteristics of rational functions) #dok3
- determine (behavior of rational functions around asymptotes) #dok2
- identify (horizontal, vertical, and oblique asymptotes) #dok2
- explain (how rational functions behave near each type of asymptote) #dok3
Learning Targets
- I can identify the horizontal, vertical, and oblique asymptotes of a rational function. #dok2
- I can determine how a rational function behaves around each type of asymptote. #dok2
- I can analyze and explain the characteristics of rational functions near their asymptotes. #dok3
- I can describe and justify how a rational function changes as it approaches its asymptotes. #dok3
Big Ideas
- Rational functions have distinctive behaviors near asymptotes that reveal important characteristics of their graphs.
- Understanding asymptotes enables us to predict and explain the behavior of rational functions in real-world and mathematical contexts.
Essential Questions
- How do you determine the locations and types of asymptotes for a rational function?
- What happens to the value of a rational function as it approaches a vertical asymptote?
- How can you predict the end behavior of a rational function using its asymptotes?
- Why do some rational functions have oblique asymptotes rather than horizontal asymptotes?
- How does analyzing asymptotes help you understand the real-world applications of rational functions?