Matter and Motion
Fall 2004
Review chart for Calculus—week 4
general topic |
recognition / standard form /
notation |
reference example |
basic operations |
Library of Functions |
|
|
• evaluate on calculator • graph on calculator • find specific member of family for specific situation |
linear |
mx+b |
temperature conversion |
|
exponential |
10x, ex |
population growth |
|
logarithmic |
log x, ln x |
inverse of exponential |
|
trigonometric |
sin x, cos x, tan x |
height of tide |
|
stretches and
shifts |
f(x-a), kf(x) |
y=k(x-a)2 |
|
inverse |
|
logarithim |
|
|
|
|
|
The Derivative Concept |
|
|
|
derivative at a
point |
f’(a), dy/dx|x=a |
speed at an instant |
estimate for given function and point, calculate exactly using limits |
derivative
function |
f’(x), dy/dx |
|
calculate exactly using limits |
A possible essay question:
For a given pair of the following concepts, give a definition of each,
and write a short paragraph explaining the connection between them and any
important distinctions between them.
the derivative at a point / the derivative function / slope of a
curve at a point / difference quotient / limit
Example: function / domain / range
A function is a rule that takes certain numbers as inputs and
assigns to each a definite output number.
The domain of a function is the set of all input numbers allowed
for that function.
The range is the set of all output numbers which that function can
generate.
Domain/Range: the domain of a function and the range of a function
are connected by the fact that each number in the domain is connected to some
number in the range. The most important distinction between them is that domain
refers to inputs and range to outputs.