Exam 1 Review (Sections 1.1 – 2.1)
MATH 1113
1. This table gives y as a function of x, with y  f (x).
a) Is 0 an input or an output of this function?
x
y  f (x)
-4 -1 0 1 3 7 12
5 7 3 15 8 9 10
b) Is f (7) an input or an output of this function?
c) State the domain and the range of this function.
d) Explain why this relationship describes y as a function of x.
e) Use the table to find y  f (4) and y  f (3) .
f) Use the table to find x when f ( x)  3.
2. If
f ( x)  16  2 x 2 , find
a)
f (3)
b) f (2)
c) f (1)
3. Tell whether each of the following equations does or does not describe y as a function of x.
Explain either why it does using the definition of function or give specific ordered pairs that
show why it does not.
a) x 2  y  10
b) x 2  y 2  1
4. Tell whether each of the following graphs does or does not describe y as a function of x.
a)
b)
5.
The number of movie admissions (in billions) in the U.S. for selected years is given in the table
below as a function of the number of years after 1980.
Years after
1980
0
5
10
15
18
Movie Admissions
(billions of people)
1.02
1.06
1.10
1.26
1.48
a) What time period is represented in this table?
b) In what year was the number of movie admissions 1.48
billion?
c) Write a sentence to explain the meaning of f (5)  1.06 in
the context of this problem.
d) What can be said about the number of admissions over this
period of time?
e) How can you be sure that the table represents a function?
6. An electric utility company determines the monthly bill by charging 10.5 cents per kilowatt-hour
(KWH) used plus a base charge of $5.80 per month.
a) Write a linear function that models cost as a function of the number of KWH.
b) Find f (1000) and explain what it means in this context.
c) What is the monthly charge if 1500 KWH are used?
7. Find the domain of each of the following functions:
x4
a) f ( x) 
b) y  2 x  6
c) f ( x)   x 2  3
x4
d) y  x 3  5x  20
8. Graph the function given in #7d using the window [-10, 10]  [-10, 10]. Then graph it again using
the window [-10, 10]  [-50, 50]. Which one shows a more complete graph?
Sketch it below.
9. Complete a table for the function f ( x)  3x 2  5x  8 for the given values of x: -8, -5, 24, 43.
10. The cost of prizes & expenses of state lotteries is given by L  35t 2  740t  1207 million dollars,
with t equal to the number of years after 1980.
a) What are the values of t that correspond to the years 1985, 1990, and 2005?
b) Find f (20) and write a sentence to explain its meaning in the context of this problem.
c) What xmin and x max should be used to set a viewing window so that the years 1980 – 2009 are
represented on the graph?
11. The rate (number per 100,000 people) of juvenile arrests for crimes is given by
f ( x)  0.027 x 2  5.69 x  51.15 , where x is the number of years after 1950.
a) Graph this function on the viewing window [0, 50] by [0, 300] and sketch your graph.
b) This viewing window shows the graph for what time period?
c) Did the rate of juvenile arrests increase or decrease over this period?
d) Use the model to find the rate of juvenile arrests in 1960 & in 1998.
12. Find the rate of change of the linear function which contains the following points.
a) (-1, -2) & (4, -12)
b) (2, 1) & (6, 3)
c) Are the lines whose slopes you found in parts (a) & (b) parallel, perpendicular or neither?
13. The per capita tax burden B (in hundreds of dollars) can be described by B(t )  20.37  1.834t ,
where t is the number of years after 1980.
a) What is the slope of the graph of this function?
b) What is the rate of growth of the per capita tax burden per year? Please give the units.
14. The cost of a business property is $700,000 and a company depreciates it using the straight line
method. Suppose y is the value of the property after x years, and the line representing the value as a
function of years passes through the points (10, 500,000) and (15, 400,000)
a) State the annual rate of change, using units in your answer.
b) Find the equation of the line that models this data.
c) Determine the y-intercept and explain its meaning, using units in your answer.
d) Determine the x-intercept and explain its meaning, using units.
15. Suppose the monthly total cost for the manufacture of golf balls is C ( x)  5400  0.73x , where x is
the number of balls produced each month.
a) Is this a linear function?
b) What is the marginal cost (rate of change of the cost function) for the product? Give units!
c) What is the cost of producing 1000 golf balls?
16. Write the equation of the line that satisfies the following conditions:
a) Zero slope and passes through (3, 6)
b) Vertical line through the point (-5, 2)
c) Through (-3, -6) & (0, 2)
d) Through (-1, 1) & (4, 3)
e) x –intercept -3 & y-intercept 1
f) Rate of change is -6 and y = 9 when x = 0.
17. Write a linear function that computes the long distance phone bill in dollars for calling t minutes at
20 cents per minute plus a fixed fee of $3.95 each month.
18. Assume that the growth of the membership of a country club was linear from 1996 to 2000 with a
membership of 181 in 1996 and a rate of growth of 699 per year. Write an equation for the
membership P of this country club as a function of the number of years t after 1996. Then use the
function to approximate the membership in 2002.
19. A business uses straight-line depreciation to determine the value V of an automobile over an 8 year
period. Suppose the original value (when t = 0) is $23,500 and the salvage value (when t = 8) is
$5000.
a) By how much has the automobile depreciated over the 8 years?
b) How much is the automobile depreciating each year? Give units!
c) Write the linear equation that models the value V of this automobile at year t.
20. A company finds that it can produce 25 heaters for $6500, while producing 45 heaters costs $9000.
Express the cost, y, as a linear function of the number of heaters, x.
21. Solve each of the given equations algebraically. You may check your answers by graphing.
x5
x 1
x 
a) 3(2 x  7)  ( x  2)  5( x  1)  4 x
b)
4
2 3
22. Solve each of the given formulas for the specified variable.
3p  n
a) Q 
for p
b) 3x  y  5m  xy for x
z
23. The equation 5F  9C  160 gives the relationship between Fahrenheit and Celsius temperature
measurements. What Fahrenheit measure is equivalent to a Celsius measurement of 50º?
24. The number of brokerage accounts on the Internet in year t can be modeled by B(t )  3.3t  6591.6
million accounts. If this model remains valid, in what year will there be 48 million accounts?
25. The percent of unmarried women who get married in any particular year is given by
y  0.0762 x  8.5284 , where x is the number of years after 1950. During what year does this
model predict the percent will be 6.09?