3.1 Functions Hwk: Std (1, 6, 9, 14, 17, …) -41, +38
Def: func is a rule that expresses a relationship between two sets of numbers. [not in book]
Specifically [from text], it consists of
set of inputs (domain)
rule by which each input determines one and only one output
set which includes the outputs (range)
Could a given table/graph/function-diagram represent a function? [build based on f(x)=x^2-2x, x=-1..3
Greatest integer function: compute values
Could a given equation represent a function?
If so, create a table of values (calc OK)
Identify "output" vs "input" from a table/graph -- [write one that has 2-3 x's for a given y (not 1-1)]
X24-25
App X27 is weight a function of postage or vice versa
X31 is price a func of "demand" (nr items sold) or vice versa
Building equations: write ___ as a func of ___
Ex: #73
3.2 Functional Notation Hwk: Std (1, 6, 9, 14, 17, …)
f(x) means [and show on a graph] func named x, & var is x. Text: output prod. by the input x
f(-1) means " " " and the var is repl by -1; " " " the input -1
f(x+h) means " " "
Ex 6 errors
find domains
piecewise defined
Ex 9 and 10 Econ func
3.3 Graphs of Functions Hwk: Std (1, 6, 9, 14, 17, …), +2, 3, 4,
Standard
What are local maxima and minima (for #21)
How to locate intervals where a func is increasing or decreasing: from graph, from eqn (start w graph)
For #34, sketch a graph from given facts
X58
3.4 Graphs and Transformations Hwk: Std (1, 6, 9, 14, 17, …)
y = f(x)±c
y=f(x±c)
y=cf(x) and -cf(x)
y=f(-x)
In general, if the modif is inside the function argument, it affects x, i.e. a horizontal effect
and, if the modif is outside the function argument, it affects y, i.e. a vertical effect
3.5 Operations on Functions Hwk: Std (1, 6, 9, 14, 17, …), +33, 44, 53, -37, 46, 49
Find (f+g)(x) etc
Ex: f(x) = sqrt(x), g(x) = x^2-3x+2
Find domains of fg and f/g
Find (f og)(4) and (g of)(4) Iterated approach
Find the "rule of the func" f og and g of and contrast with fg
[For inverses only] Show that (f og)(x) = x and (g of)(x) = x for every x Not true for funcs in general
Write a given func as the compos of two funcs
Ex: #43 and 45
3.6 Average Rates of Change Hwk: Std (1, 6, 9, 14, 17, …)
Def: = chg in f(x) / chg in x = (f(b)-f(a)) / (b-a)
From formula, or from graph, or from table
Geometrically, slope of secant line
So: interpret rates of change as slopes of tangent lines
Ex Chipmunks and predators, X23
X26 obsv: slope of regression line is avg rate of change
Return to: Merced College; Don Power Updated 08/16/05 by Don Power