Rational functions (AA HL 2.13) (Linear over quadratic)
 Author:
 Cliff Packman
 Topic:
 Functions
Keywords
Rational Function  有理関数  유리 함수  有理函数 
Vertical Asymptotes  垂直漸近線  수직 점근선  垂直渐近线 
Domain  定義域  정의역  定义域 
Horizontal Asymptote  水平漸近線  수평 점근선  水平渐近线 
Simplify  簡単化  단순화  简化 
Degree of Numerator and Denominator  分子と分母の次数  분자와 분모의 차수  分子和分母的次数 
Holes (Removable Discontinuities)  穴（取り除ける不連続性）  구멍 (Removable Discontinuities)  孔（可去不连续性） 
Transformations  変換  변환  变换 
Intercepts  切片  절편  截距 
Inquiry questions
Factual Questions
 Conceptual Questions
 Debatable Questions

1. What patterns do you notice in the graph when the coefficients of the quadratic in the denominator are altered?
2. How does changing the coefficient 'a' in the numerator (ax + b) impact the graph of the function? Consider both positive and negative values.
3. Identify the vertical asymptotes of the function and relate them to the denominator's factors. How do they shift when you tweak 'c', 'd', and 'e'?
4. Examine the horizontal asymptote or the end behavior of the function. What happens as x approaches positive or negative infinity?
5. Can you find a set of coefficients where the graph crosses the horizontal asymptote?
6. Challenge: Create a scenario where the function has a "hole" (a removable discontinuity). What condition on the coefficients would lead to this situation?