Rational Functions.

🧩 Flashcards (20 Total)

#	Concept	Front	Back
1	Rational Function	What is a rational function?	A fraction made of two polynomials P(x)Q(x)Q(x)P(x) where Q(x)≠0Q(x)=0.
2	Simplify	What do you always do first?	Simplify the expression — cancel common factors.
3	V.A.	How do you find vertical asymptotes?	Set denominator = 0 after simplification.
4	V.A. rule	When is a value NOT a vertical asymptote?	When it’s a hole (factor cancels).
5	H.A. rule 1	If degree top < degree bottom?	y=0y=0.
6	H.A. rule 2	If degree top = degree bottom?	y=leading coeff numeratorleading coeff denominatory=leading coeff denominatorleading coeff numerator.
7	H.A. rule 3	If degree top > degree bottom?	No H.A. (check for slant).
8	S.A.	When does a slant asymptote occur?	When degree of numerator = degree of denominator + 1.
9	S.A. method	How do you find a slant asymptote?	Use long division (quotient = asymptote).
10	X-Int	How do you find x-intercepts?	Set numerator = 0 (after simplification).
11	X-Int check	What must you check after solving numerator = 0?	That x doesn’t make denominator = 0.
12	Y-Int	How do you find the y-intercept?	Plug in x=0x=0.
13	Holes	When do holes occur?	When a factor cancels between numerator and denominator.
14	Holes (x)	How to find x of a hole?	Set the cancelled factor = 0.
15	Holes (y)	How to find y of a hole?	Plug x of hole into simplified function.
16	Step order	What’s the best order to analyze?	Simplify → Holes → V.A. → H.A./S.A. → X-Int → Y-Int.
17	Degrees	What does “degree” mean?	The highest power of x in the polynomial.
18	Coefficients	What is the “leading coefficient”?	The number in front of the highest-power x term.
19	Graph meaning	What do asymptotes represent?	Lines the graph approaches but never touches.
20	Domain reminder	What x-values are excluded?	Any x that makes the denominator 0.