For graphing problems, you have to show work (e.g., plot
specific points).
You won’t get much credit if it looks like
you could have just copied your picture from the output of
a graphing calculator.
Key concepts of section 1.1:
Function, domain, range
Increasing, decreasing, even, odd
[Have the students define these.]
Function: A
function
f
is a rule that associates values of
y
with values of
x
, so that each value of
x
is associated with
at most one value of
y
.
(Why “at most one value?”
Differential calculus – the subject of 92.141 – is about how
a change in one variable effects another variable.
It’s best
suited to situations in which the value of one variable,
x
,
completely determines the value of another variable,
y
; we
call
x
and
y
the
independent
and
dependent
variables,
respectively.
Later we’ll see how the methods can be
applied to situations where
x
does not completely determine
y
, as in the case of the circle
x
2
+
y
2
= 1 for instance.)
Example:
f
(
x
) = 1 – 1/
x
is a function of
x
(it has one value
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x
is nonzero, and no values when
x
is zero).
Nonexample:
g
(
x
) =
±
sqrt(
x
) is not a function of
x
(it has
two values when
x
is positive).
Domain: The
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 Fall '11
 Staff
 Calculus, Probability theory, Order theory, Monotonic function, Convex function

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