Unit 6
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Unit 6: Limits, Continuity (连续性), and Rational Functions
Lesson 1: Introduction to Rational Functions and Limits
Rational functions (有理函数): quotient of polynomial functions
f(x)=N(x)/D(x) , where N(x) and D(x) are polynomials and D(x)≠0
Asymptotes
Limits (极限)and asymptotes
Discontinuities: Holes vs. vertical asymptotes
Lesson 2: Operations with Rational Functions and Rate Problems
Adding, subtracting, multiplying, dividing.
Simplifying complex functions
Solving rational equations
Function composition f(g(x))
Domain and range
Problem solving with rates
Lesson 3: Limits and Continuity
When does limit exist?
Function continuity
Lesson 4: Graphs of Reciprocal Functions and Horizontal Asymptotes
Graphs of reciprocal functions
Steps
Reciprocal trigonometric graphs
Horizontal asymptotes
Proper rational form
Location of horizontal asymptotes
Lesson 5: Slant asymptotes and end behavior
Slant asymptotes
End behavior of rational functions
Lesson 6: Graphing and Writing Equations for Rational Functions
Steps for graphing:
Factor f(x)
Graph all asymptotes
Cancel common factors
Use limits to determine the end behavior
Steps for writing equations:
Identify x-ints, holes, and VA
Use equation: