1.E: Review (Exercises)
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- Jan 11, 2024
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1.1 Exercises
Exercise
The amount of garbage,
- The town of Tola has a population of 40,000 and produces 13 tons of garbage each week. Express this information in terms of the function
. - Explain the meaning of the statement
.
Exercise
The number of cubic yards of dirt,
- A garden with area 5000
requires 50 cubic yards of dirt. Express this information in terms of the function . - Explain the meaning of the statement
.
Exercise
Select all of the following graphs which represent






Exercise
Select all of the following graphs which represent






Exercise
Select all of the following tables which represent
a.
x |
5 |
10 |
15 |
y |
3 |
8 |
14 |
b.
x |
5 |
10 |
15 |
y |
3 |
8 |
8 |
c.
x |
5 |
10 |
10 |
y |
3 |
8 |
14 |
Exercise
Select all of the following tables which represent
a.
x |
2 |
6 |
13 |
y |
3 |
10 |
10 |
b.
x |
2 |
6 |
6 |
y |
3 |
10 |
14 |
c.
x |
2 |
6 |
13 |
y |
3 |
10 |
14 |
Exercise
Given the function
- Evaluate
- Solve

Exercise
Given the function
- Evaluate
- Solve

Exercise
Based on the table below,
- Evaluate
- Solve
x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
74 |
28 |
1 |
53 |
56 |
3 |
36 |
45 |
14 |
47 |
Exercise
Based on the table below,
- Evaluate
- Solve
x |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
|
62 |
8 |
7 |
38 |
86 |
73 |
70 |
39 |
75 |
34 |
Exercises
For each of the following functions, evaluate:
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Exercise
Let
- Evaluate
- Solve
Exercise
Let
- Evaluate
- Solve
Exercise
Using the graph shown,
- Evaluate
- Solve
- What are the coordinates of points
and ?
Exercise
Match each graph with its equation.
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b. |
d. |
|
e. |
f. |
g. |
h. |








For Exercises
Exercise

Exercise

Exercise
Find the domain of each function.
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1.2 Exercises
Exercise
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4. |
Exercise
x |
|
|
0 |
7 |
9 |
1 |
6 |
5 |
2 |
5 |
6 |
3 |
8 |
2 |
4 |
4 |
1 |
5 |
0 |
8 |
6 |
2 |
7 |
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1 |
3 |
8 |
9 |
4 |
9 |
3 |
0 |
Use the table of values to evaluate each expression.
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Exercise


Use the graphs to evaluate the expressions below.
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Exercise
For each pair of functions, find
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Exercise
If
Exercise
If
Exercise
The function
- Evaluate
- Solve
- Evaluate
- Solve
Exercise
The function
- Evaluate
- Solve
- Evaluate
- Solve
Exercise
Find functions
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Exercise
Sketch a graph of each function as a transformation of a toolkit function.
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Exercise
Write an equation for each function graphed below.






Exercise
For each function graphed, estimate the intervals on which the function is increasing and decreasing.


1.3 Exercises
Exercise
A town's population has been growing linearly. In 2003, the population was 45,000, and the population has been growing by 1700 people each year. Write an equation,
Exercise
A town's population has been growing linearly. In 2005, the population was 69,000, and the population has been growing by 2500 people each year. Write an equation,
Exercise
Timmy goes to the fair with $40. Each ride costs $2. How much money will he have left after riding
Exercise
At noon, a barista notices she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves
Exercise
A phone company charges for service according to the formula:
Find and interpret the rate of change and initial value.
Exercise
A phone company charges for service according to the formula:
Find and interpret the rate of change and initial value.
Exercise
Given each set of information, find a linear equation satisfying the conditions, if possible.
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8. |
9. Passes through (2,4) and (4,10) | 10. Passes through (1, 5) and (4, 11) |
11. Passes through (-1,4) and (5, 2) | 12. Passes through (-2, 8) and (4, 6) |
13. |
14. |
Exercise
Find an equation for the function graphed.


Exercise
A clothing business finds there is a linear relationship between the number of shirts,
Exercise
A farmer finds there is a linear relationship between the number of bean stalks,
Exercise
Match each linear equation with its graph
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Exercise
Sketch the graph of each equation
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Exercise
Find the point at which the line
Exercise
Find the point at which the line
Exercise
A car rental company offers two plans for renting a car.
Plan A: 30 dollars per day and 18 cents per mile
Plan B: 50 dollars per day with free unlimited mileage
How many miles would you need to drive for plan B to save you money?
Exercise
A cell phone company offers two data options for its prepaid phones
Pay per use: $0.002 per Kilobyte (KB) used
Data Package: $5 for 5 Megabytes (5120 Kilobytes) + $0.002 per addition KB
Assuming you will use less than 5 Megabytes, under what circumstances will the data package save you money?
Exercise
The Federal Helium Reserve held about 16 billion cubic feet of helium in 2010, and is being depleted by about 2.1 billion cubic feet each year.
- Give a linear equation for the remaining federal helium reserves,
, in terms of , the number of years since 2010. - In 2015, what will the helium reserves be?
- If the rate of depletion doesn’t change, when will the Federal Helium Reserve be depleted?
Exercise
Suppose the world's current oil reserves are 1820 billion barrels. If, on average, the total reserves is decreasing by 25 billion barrels of oil each year:
- Give a linear equation for the remaining oil reserves,
, in terms of , the number of years since now. - Seven years from now, what will the oil reserves be?
- If the rate of depletion isn’t change, when will the world’s oil reserves be depleted?
1.4 Exercises
Exercise
Simplify each expression
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3. |
4. |
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8. |
Exercise
Simplify, and rewrite without negative exponents
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Exercise
Rewrite using negative or fractional exponents
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Exercise
Rewrite as a radical
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1.5 Exercises
Exercise
Write an equation for the quadratic function graphed.






Exercise
7. |
8. |
9. |
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Exercise
The height of a ball thrown in the air is given by
- How high is the ball when it was thrown?
- What is the maximum height of the ball?
- How far from the thrower does the ball strike the ground?
Exercise
A javelin is thrown in the air. Its height is given by
- How high is the javelin when it was thrown?
- What is the maximum height of the javelin?
- How far from the thrower does the javelin strike the ground?
1.6 Exercises
Exercise
Find the degree and leading coefficient of each polynomial
1. |
2. |
3. |
4. |
5. |
6. |
Exercise
Find the vertical and horizontal intercepts of each function.
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8. |
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11. |
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Exercise
Use your calculator or other graphing technology to solve graphically for the zeros of the function.
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14. |
Exercise
Solve each inequality.
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17. |
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Exercise
For each function, find the horizontal intercepts, the vertical intercept, the vertical asymptotes, and the horizontal asymptote.
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Exercise
A scientist has a beaker containing 20 mL of a solution containing 20% acid. To dilute this, she adds pure water.
- Write an equation for the concentration in the beaker after adding
mL of water. - Find the concentration if 10 mL of water has been added.
- How many mL of water must be added to obtain a 4% solution?
- What is the behavior as
, and what is the physical significance of this?
Exercise
A scientist has a beaker containing 30 mL of a solution containing 3 grams of potassium hydroxide. To this, she mixes a solution containing 8 milligrams per mL of potassium hydroxide.
- Write an equation for the concentration in the tank after adding
mL of the second solution. - Find the concentration if 10 mL of the second solution has been added.
- How many mL of water must be added to obtain a 50 mg/mL solution?
- What is the behavior as
, and what is the physical significance of this?
1.7 Exercises
Exercise
A population numbers 11,000 organisms initially and grows by 8.5% each year. Write an exponential model for the population.
Exercise
A population is currently 6,000 and has been increasing by 1.2% each day. Write an exponential model for the population.
Exercise
A vehicle purchased for $32,500 depreciates at a constant rate of 5% each year. Determine the approximate value of the vehicle 12 years after purchase.
Exercise
A business purchases $125,000 of office furniture which depreciates at a constant rate of 12% each year. Find the residual value of the furniture 6 years after purchase.
Exercise
If $4,000 is invested in a bank account at an interest rate of 7 per cent per year, find the amount in the bank after 9 years if interest is compounded annually, quarterly, monthly, and continuously.
Exercise
If $6,000 is invested in a bank account at an interest rate of 9 per cent per year, find the amount in the bank after 5 years if interest is compounded annually, quarterly, monthly, and continuously.
Exercise
Match each function with one of the graphs below.
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8. |
9. |
10 |
11. |
12. |
Exercise
If all the graphs to the right have equations with form
13. Which graph has the largest value for |
14. Which graph has the smallest value for |
15. Which graph has the largest value for |
16. Which graph has the smallest value for |
1.8 Exercises
Exercise
Rewrite each equation in exponential form
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2. |
3. |
4. |
Exercise
Rewrite each equation in logarithmic form.
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Exercise
Solve each equation for the variable.
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Exercise
The population of Kenya was 39.8 million in 2009 and has been growing by about 2.6% each year. If this trend continues, when will the population exceed 45 million?
Exercise
The population of Algeria was 34.9 million in 2009 and has been growing by about 1.5% each year. If this trend continues, when will the population exceed 45 million?
Exercise
If $1000 is invested in an account earning 3% compounded monthly, how long will it take the account to grow in value to $1500?
Exercise
If $1000 is invested in an account earning 2% compounded quarterly, how long will it take the account to grow in value to $1300?
Exercise
Sketch a graph of:
Exercise
Find the domain of each function.
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