Math 121
Fall 2010
Final Exam Review
PLEASE NOTE: You must show work on exam to receive credit.
1. Find an equation of the linear function which:
a. passes through the points (-2,-3) and (4,1).
b. is vertical and passes through
2
, 1
3
−
.
c.
is horizontal and passes through (-4,5).
d.
is perpendicular to
4 7
x y
+ =
and passes through (1,3).
2.
A small appliance manufacturer finds that it costs $9000 to produce 1000 toaster ovens a
week and $12,000 to produce 1500 in a week.
a.
Assuming the relationship is linear, express the cost,
C
, as a function of the
number of toaster ovens produced,
x
.
b.
Find the vertical intercept. What does it represent in the context of this problem?
c.
Explain the slope in the context of this problem.
3.
Solve the system of inequalities
5 3 10
y x
+ ≤
and
5 10
y x
− ≥ −
by graphing. Make sure
to label the vertical intercepts and the intersection point. Clearly show all work.
4.
Solve the following systems of two linear equations algebraically, either by substitution
or elimination.
5.
The tax code in a particular state requires residents to pay 15% income tax on the first
$30,000 they earn and 25% on any income above that level. Find a piecewise linear
function that gives the amount of tax owed as a function of income. Graph the function,
labeling the axes appropriately.
6.
A large wholesale nursery sells shrubs to retail stores. Their cost
( ) 15 12,000
C x x
= +
and revenue
( ) 18
R x x
=
where
x
is the number of shrubs sold. What is the breakeven
point?
7.
Use the conversion chart in the back of your book to solve the following conversion
problems
a.
How many fluid ounces are there in a 2 liter bottle of coke?
b.
If you make $45,000 per year, what is your salary in dollars/hour, assuming a 40
hour work week and 52 weeks per year?
3
2
2( ) 1
x
y
x y y
+ =
+ = −
4 3 3
5 2 9.5
x y
x y
+ =
− =
