Precalculus II
Topics:
- Link to course syllabus.
- A short course on Trigonometry
- Useful tool for graphing. (Desmos).
- Wolfram Alpha.
- Line equations
- Exercise 1: You are about to take a trip and you plan to rent a car, here are two rental offers: (i) Hertz will give you 30 cents per mile and $45 per day, and (ii) Avis will give you 25 cents per mile and $50 per day. Suppose you decide to rent a car for 4 days. Which company offers you a better deal? Explain. Answer.
- Exercise 2: A manufacturer of electronic components finds
that in making x units of a prduct weekly it has a cost of $2 per unit,
plus a fixed cost of $1800. Each unit sells for $5.
(a) Find the cost, revenue and profit functions.
(b) Sketch these functions.
(c) Find the break-even point.
(d) Find the total weekly revenue at the break-even point. - Check your notes for C-F problems: Do you know Celsius would meet Fahrenheit at some point? Where?
- Finding Domain of a function and Shifting
- Drills of finding domain of a function.
- Shifting and Reflection Techniques:
- Practices
on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
- Horizontal Shifting: y = f(x + a) is a horizontal shifting of y = f(x). If a > 0, then the graph will be shifted to the left; if a <0, then the graph will be shifted to the right.
- Vertical Shifting: y = f(x) + a is a vertical shifting of y = f(x). If a > 0, then the graph will be shifted up; if a <0, then the graph will be shifted down.
- y = - f(x) is a reflection of y = f(x).
- Extra Credits
- Composition of Functions
- Inverse functions
- Practice on composite and inverse functions.
- Solution is here.
- Practices
on shifting, expansion and etc. (a PDF file). (**Hints/solutions)
- Circle .
- Unit Circle .
- Sine, Cosine and Tangent (reading)
- (VIP) Interactive Unit Circle.
- Exercises
- About the graphs of trig functions.
- Exercises; (answer is on the same page).
- Define the function f whose graph is similar to a "sine" function
and satisfies the following conditions
- The period of f is 180 degree.
- The function f has the amplitude of 3.
- The function f has the highest value of 0 at x=135 degree.
- Practice problems
- Review for an old test..
-
Trigonometric substitutions.
- More on Trig. Subs.
- Review for an old Final.