[Go around with names]
[Hand out time sheets]
Section 1.2
What’s the main point of section 1.2?
..?.
.
Functions that crop up in the real world can be represented or
at least approximated by functions that are algebraically built
up from some universal building blocks.
If we can understand
the building blocks, we can understand the functions that are
built from them, and their graphs.
Building blocks: linear functions, polynomials, rational
functions (built from polynomials), trig and exponential
functions, and logarithms.
Combination rules: You can add, subtract, multiply, or
divide two functions to get a new function; or you can
compose
two functions to get a new function.
(
f
+
g
)(
x
) =
f
(
x
)+
g
(
x
)
(
f
–
g
)(
x
) =
f
(
x
) –
g
(
x
)
(
f
g
)(
x
) =
f
(
x
)
g
(
x
)
(
f
/
g
)(
x
) =
f
(
x
)/
g
(
x
)
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f
°
g
)(
x
) =
f
(
g
(
x
))
Q. Is there a way to express
y
=
x
 in terms of standard
algebraic operations, as a
single
algebraic expression?
..?.
.
A. sqrt(
x
2
)
Q. Is there an algebraic function whose value is +1 for
positive values of
x
and –1 for negative values of
x
?
...
A. (sqrt(
x
2
))/
x
.
Q. (continuation of preceding question) Is there an
algebraic function whose value is +1 for positive values of
x
, –1 for negative values of
x
, and 0 for
x
=0?
..?.
.
A. To be continued!
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 Fall '11
 Staff
 Calculus, Algebra, Quantification, good people, SQRT, Quantifiers Quantifiers

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