Functions and Models

Some time ago I finished walking through chapter one of James Stewart's Calculus, "Functions and Models."  Right now I'm snailing through chapter 2 at 2 pages a day.  But I wanted to catch-up with myself by making a review sheet for chapter 1.

• Tangent problem and area problem generated calculus (differential the first and integral the second).  Sum of a series relates to the second.
• What is a function, domain, range, etc?  Basically, exactly one y for each element in x (thus the vertical line test--a vertical line can't ever pass through a function more than once.
• Piecewise functions have parts.  An even function is symmetrical with regard to the y axis (f of x=f of -x).  An odd function has symmetry with regard to the origin (f of x= negative of f of -x).
• Linear functions are of the form y=mx+b (slope intercept form).
• Polynomial functions involve powers of x beyond the first.  Quadratic involves the second degree (x squared).  Cubic functions involve the third (x cubed).
• More polynomial functions include power functions of the form x to the a power, where a is a constant.  The root function is x raised to the 1/n power (e.g., the 1/2 power is a square root).  A reciprocal function is something raised to a negative power, which means one over that x to a positive power.
• Rational functions are of the form P(x)/Q(x).
• Algebraic functions can be put into the form of algebraic operations (add, subtract, etc), such as all those that precede.
• Transcendental functions are non-algebraic and are the ones that follow.
• Trigonometric functions involve things like sine and cosine.
• Exponential functions involve a constant raised to the power x.  Logarithmic functions are the inverse y=log base a of x.
• Then we have the translations I think I covered somewhere below from the pre-calculus text.  Don't feel like repeating them.  Same with stretching and reflecting functions, composite functions.
• The sections I'm seeing on graphing calculators in this book are truly fascinating because it just shows how old I am.  We had nothing like this on the Texas Instrument calculators I used to think were off the charts because they did logarithms and the trig. functions.