MA 139 TEST 1 REVIEW
FORMULAS
21
21
yy
mxx
−
=−
11
()y y mx x−= −
0
( ) ()
( ) lim
h
fx h fx
fx h
→
+−
′=
[ ]
() () () () () ()
dfxgx fxgx fxgx
dx ′′
⋅ = ⋅+⋅
[ ]
2
() () () () ()
() ()
d fx f x gx fx gx
dx g x gx
′′
⋅−⋅
=
1.) Find the slope of the line containing the points (-2, 3) and (4, -1).
2.) For the line
23 4xy+=
, give the corresponding change in y if:
a.) x increases by 4 b.) x decreases by 2
3.) Find the equation of the line with slope of
4
3
−
and containing the point (5, 2). Give answer in slope-
intercept form.
4.) Find the domains of each of the following functions: a.)
32
() 6 3hx x x= +−
b.) () 2 5gx x= − c.)
2
2
4
() 26
x
fx xx
−
=+−
d.) 5/2
( ) (8 1)Px x= +
e.)
2 2/3
( ) (5 )hx x x= −
5.) Given
2
() 2fx x x= −
and
() 3gx x= −
find each of the following: a.)
( )( )fg x
b.)
( )( )g fx−
c.)
( )( )fgx
d.)
( )(3)fg
6.) Find functions f and g such that
hgf=
for
24
3
() (2 1)
hx x
=−.
7.) A manufacturer has a monthly fixed cost of $20,000 and a production cost of $8 per unit. Each unit sells for
$12. Find each of the following:
a.) the cost function
b.) the revenue function
c.) the profit function
d.) the profit or loss corresponding to a production level of 3500 units.
8.) Graph
2
2 1
() 3 1 1
x if x
fx x if x
−<
=+≥
(give coordinates of points on each part of the graph) and find
1
lim ( )
xfx
→
, if it exists, or state that it does not exist.
9.) Evaluate each of the following limits, if they exist, or state that they do not exist:
a.)
2
3
lim 4 1
x
xx
→
−+
b.)
1
lim 7
x→−
c.) 2
42
2 94
lim
16
x
xx
x
→
−+
−
d.)
32
24
lim 9
x
x
x
→
−
−
e.)
2
2
2
lim 2
x
x
x
−
→
−
+
f.)
9
9
lim 3
x
x
x
→
−
−
g.)
3
3
51
lim 3 22
x
x
xx
→−∞
−
++
h.)
2
2
lim 4
x
x
x
→∞
+
−
i.) 2
44
limx
x
x
→∞
+
