NAME:
TEST1A/MAC2311 Page 1 of 5
Read Me First:
Show all essential work very neatly. Use
correct notation when presenting your computations and arguments.
Write using complete sentences. Be careful.
Remember this: "="
denotes "equals" , "
⇒
" denotes "implies" , and "
⇔
" denotes "is
equivalent to".
Since the answer really consists of all the
magic transformations, do not "box" your final results.
Communicate. Show me all the magic on the page.
1. (10 pts.)
On the coordinate system below sketch the graph of
the function g defined below. Label very carefully.
x
,
x
≥
1 or x
≤
1
g(x) =
x
2
,
1 < x < 1
y
x
2. (10 pts.) If f(x) = 4x
2
 6x, find
f(x + h)  f(x)
,
h
and simplify as much as possible algebraically. Kindly observe
that there are no limits of any sort being taken here.
f(x + h)  f(x)
=
h
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TEST1A/MAC2311 Page 2 of 5
3. (5 pts.) Using complete sentences and appropriate notation,
provide the precise mathematical definition of a
function
f //
4. (10 pts.)
Suppose f(x) = x
2
+ 8 and g(x) = (x  8)
1/2
.
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 Fall '08
 STAFF
 Calculus, Limit, lim, pts, Continuous function

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