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Home on the Range Part 1
Home on the Range Part 1
Indicate the answer choice that best completes the statement or answers the question.
Express each relation as a graph and a mapping. Then determine the domain and range.
1. {(1, –2), (–2, –3), (2, 4), (1, –4)}
a.
D = {–2, 1, 2}; R = {–4, –3, –2, 4}
b.
D = {–2, 1, 2, 4}; R = {–4, –3, –2}
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Home on the Range Part 1
c.
D = {–2, 1, 2}; R = {–4, –3, –2, 4}
d.
D = {–2, 1, 2}; R = {–4, –3, –2, 4}
A soft drink bottle filling machine can fill 22 bottles per minute. The table shows the relationship
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Home on the Range Part 1
between the number of minutes and the number of bottles filled.
Time (minutes)
Bottles filled
1
22
2
44
3
66
4
88
5
110
2. Use the soft drink bottle table to predict how many bottles will be filled after seven minutes.
a. 154 bottles
b. 144 bottles
c. 176 bottles
d. 150 bottles
____3. Express the relation shown in each table, mapping, or graph as a set of ordered pairs. Then determine the
domain and range.
x
0
5
10
15
20
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y
0
2
6.5
9
11.5
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Home on the Range Part 1
4.____
11. A company increases the salaries of its employees every year by 15%. The graph shows the salary of a
particular employee as the number of years increase.
Does the graph represent a function? Explain. Describe how real-world situations can be modeled using graphs
and functions.
5. Find the inverse of the relation.
{(6, –3), (5, 1), (4, –10), (–8, 7)}
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Home on the Range Part 1
6.
a.
Graph the variation if y varies inversely as x.
when
b.
c.
d.
Solve the problem of exponential growth.
7. A company had a profit of $823,500 in 2010. This is a 26% increase from 2005. What was the company's profit
in 2005? Round to the nearest hundred.
a. $653,600
b. $802,300
c. $1,037,600
d. $572,900
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Home on the Range Part 1
Translate the sentence into an equation.
8. Three times the sum of a and b is equal to five times c.
a.
b.
c.
d.
9.
The air traffic controller schedules the take off time of 5 flights in an hour at an airport.
Flight
Flight 1
Flight 2
Flight 3
Flight 4
Flight 5
Time (P.M.)
12:10
12:20
12:30
12:40
12:50
a. How are rational equations important in the operation of flights at the airports?
b. Include in your answer an explanation of how rational equations can be used to approximate the time that
planes will pass each other if they leave distant airports and head towards each other.
____________________________________________________________________________________________________
10. A rectangle is 8 meters wide and 12 meters long. Find the height of a triangle with a base 6 meters long and an
area equal to that of the rectangle.
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Home on the Range - Part 1
Indicate the answer choice that best completes the statement or answers the question.
Graph the function. Find the y-intercept and state the domain and range.
11..
a.
b.
y-intercept = 1
domain: all real numbers
range: y > 0
y-intercept = 1
domain: all real numbers
range: y > 0
d.
c.
y-intercept = 4
domain: all real numbers
range: y > 0
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y-intercept = 3
domain: all real numbers
range: y > 0
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Home on the Range - Part 1
Pick the correct graph for
12. f(x) = 2√x +4
a.
b.
c.
d.
13. Describe the transformation from the parent function and state the domain and range.
5.
_____________________________________________________________________________________________
_____________________________________________________________________________________________
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Home on the Range - Part 1
14. This year, a school district has a budget of $58 million. The school board has voted to increase
the budget by only 1.1% each year.
a. Explain how the exponential growth can be used to predict the future budget.
b. Explain the equation
.
c. Estimate the school budget after 10 years.
______________________________________________________________________________________
______________________________________________________________________________________
______________________________________________________________________________________
15. Write the function and state the domain and range.
_____________________________________________________________________________________
_____________________________________________________________________________________
_____________________________________________________________________________________
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Home on the Range - Part 1
. Indicate the answer choice that best completes the statement or answers the question.
Graph the rational function.
16. f(x) =
a.
b.
c.
d.
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17. When Mark was 2 years old, his parents invested $2000 in a money market account
with annual average interest rate of 8%. After 15 years, how much money will he
have in the account?
____ 18. Graph the following y
a.
c.
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–2
+ –2
b.
d.
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Home on the Range - Part 1
19. According to the U.S. Census Bureau, the population of California in 2010 was 37.3 million.
This is a 10.4% increase over the 2000 count. Assuming this continued what would the
population be in 2030?
a. 50.2 million
b. 41.2 million
c. 45.5 million
d. 42.9 million
20. A box is made from a rectangular metal sheet by cutting four equal squares from the corners. The
dimensions of the box are shown below. Write an equation for the area of the sheet required to make
the box.
____21 . Find the first five terms of the sequence in which a1 = 12 and an = –2an – 1 + 4, if n ≥ 2.
a. –20, 44, –84, 172, –340
b. 2, 0, –2, –4, –6
c. 28, 12, –20, 44, –84
d. 12, –20, 44, –84, 172
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Home on the Range - Part 1
22. The table shows the amount of money in a savings account after several weeks.
Week
Savings
1
$125
2
$140
3
$155
4
$170
5
$185
6
$200
a. Is the sequence arithmetic or geometric? Explain. Find the common difference or common
ratio.
b. Write a recursive formula for the sequence.
c. Write an explicit formula for the sequence.
23. Write a recursive formula for an = –8n + 7.
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