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Clark and Anfinson - Intermediate Algebra 2/e (Homework)

James Finch

Math - Developmental, section A, Fall 2019

Instructor: Dr. Friendly

Current Score : 3 / 54

Due : Monday, December 30, 2030 23:59 EST

Last Saved : n/a Saving...  ()

Ask Your Teacher Extension Requests Print Assignment
Question
Points
1 2 3 4 5 6 7 8 9 10
3/3 –/4 –/10 –/2 –/10 –/1 –/7 –/5 –/6 –/6
Total
3/54 (5.6%)

  • Instructions

    Intermediate Algebra: Connecting Concepts Through Applications, 2nd edition, by Mark Clark and Cynthia Anfinson and published by Cengage Learning, shows students how to apply traditional mathematical skills in real-world contexts. The emphasis on skill building and applications engages students as they master concepts, problem solving, and communication skills. It modifies the rule of four, integrating algebraic techniques, graphing, the use of data in tables, and writing sentences to communicate solutions to application problems. The authors have developed several key ideas to make concepts real and vivid for students. First, the authors integrate applications, drawing on real-world data to show students why they need to know and how to apply math. The applications help students develop the skills needed to explain the meaning of answers in the context of the application. Second, they emphasize strong algebra skills. These skills support the applications and enhance student comprehension. Third, the authors use an eyeball best-fit approach to modeling. Doing models by hand helps students focus on the characteristics of each function type. Fourth, the text underscores the importance of graphs and graphing. Students learn graphing by hand, while the graphing calculator is used to display real-life data problems. In short, Intermediate Algebra: Connecting Concepts Through Applications takes an application-driven approach to algebra, using appropriate calculator technology as students master algebraic concepts and skills.

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1. 3/3 points  |  Previous Answers ClarkIAlg2 4.2.012. My Notes
Question Part
Points
Submissions Used
1 2 3
1/1 1/1 1/1
1/100 1/100 2/100
Total
3/3
 
This is an example of a question with a Watch It help resource.

Some exercises contain Watch Its. Watch Its let students see how to solve a similar problem. The variations in the randomizations ensure that a Watch It never gives away the answer.

Clark/Anfinson Pedagogical Focus
  • Reading the characteristics of graphs
Refer to the given graph to answer the questions. Assume the function is written in the vertex form of a quadratic function.
The x y-coordinate plane is given. The curve enters the window in the third quadrant, goes up and right becoming less steep, crosses the x-axis at approximately x = −3.9, passes through the point (−3.5, 1), changes direction at the point (−1.5, 3), goes down and right becoming more steep, crosses the y-axis at approximately y = 1.88, passes through the point (0.5, 1), crosses the x-axis at approximately x = 0.9, and exits the window in the fourth quadrant.
(a)
Which point is the vertex?
(x, y) = 
 Correct: Your answer is correct.
(b)
What is the equation of the axis of symmetry?
x=−1.5
Correct: Your answer is correct.
(c)
What is the symmetric point to the point
(−3.5, 1)?
(x, y) = 
 Correct: Your answer is correct.

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2. –/4 points ClarkIAlg2 4.2.026.MI. My Notes
Question Part
Points
Submissions Used
1 2 3 4
–/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100
Total
–/4
 
This is an exercise with a Master It tutorial and a solution.

The Master It question type is also embedded as an optional help type for the same base question. Only the final answer is scored in the gradebook.

This question also has a solution, which can appear after a given number of submissions or after the assignment due date, based on the instructor's settings. Enter any correct answer to see the solution.
  • Utilizes the graphing tool

Sketch the graph of the given function.
f(x) = (x − 5)2 + 4
No Solution
Help
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Clear Graph
Delete Layer
Fill

Graph LayersToggle Open/Closed

  • After you add an object to the graph you can use Graph Layers to view and edit its properties.

Identify the vertex, vertical intercept, and the point symmetric to the given point.
vertex     
(x, y) = 
vertical intercept     
(x, y) = 
point symmetric to
(x, y) = (4, 5)
    
(x, y) = 

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3. –/10 points ClarkIAlg2 4.2.036. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/10
 
Clark/Anfinson Pedagogical Focus
  • This is an application involving units, writing complete sentence answers, interpreting information in context.
  • Finding the domain and range of a function in the context of an application.

The total number of people, in thousands, who were below the poverty level can be modeled by
N(t) = −308(t − 12)2 + 46,594,
where
N(t)
 represents the total number of people in the United States who were below the poverty level, in thousands, t years since 2000.†Source: Model based on data from the U.S. Census Bureau.
(a)
How many people were below the poverty level in 2010? (Include units in your answer. More information.)
In 2010, there were about below the poverty level in the United States.
(b)
Find N(13) and explain its meaning. (Include units in your answers as appropriate. More information.)
In the year there were about below the poverty level in the United States.
(c)
Sketch a graph of this model.

(d)
Estimate the vertex of this model and explain its meaning. (Include units in your answers as appropriate. More information. Round your second answer to the nearest thousand people.)
According to this model, in the year there were about below the poverty level in the United States which is a .
(e)
Use your graph to estimate when the number of people in the United States below the poverty level was 43 million. (Round your answers to the nearest year.)
According to the graph, in about the year (smaller value) and again in the year (larger value) the number of people in the United States below the poverty level was 43 million.
(f)
If the domain for this model is
[3, 18],
 find the range.
    
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4. –/2 points ClarkIAlg2 4.2.054.MI. My Notes
Question Part
Points
Submissions Used
1 2
–/1 –/1
0/100 0/100
Total
–/2
 
Clark/Anfinson Pedagogical Focus
  • Students find the domain and range of a quadratic function from a graph.
  • Students will use interval notation.

Find the domain and range of the function. Write the answer using interval notation.
The x y-coordinate plane is given. The curve enters the window in the third quadrant, goes up and right becoming less steep, crosses the x-axis at approximately x = −0.9, crosses the y-axis at y = 8, changes direction at the point (4, 24), goes down and right becoming more steep, crosses the x-axis at approximately x = 8.9, and exits the window in the fourth quadrant.
Domain:
    
Range:
    

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5. –/10 points ClarkIAlg2 4.2.080.MI.SA. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7 8 9 10
–/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/10
 
This is an assignable Master It tutorial exercise.

This exercise guides the student through a series of steps which appear one at a time, offering guidance as it walks students through the problem-solving process. Consider placing these questions at the beginning of assignments to prepare students for success.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

Tutorial Exercise
Sketch the graph of the given function. Identify the vertex, vertical intercept, and the point symmetric to the given point. Find the domain and range of the function.
h(d) = −0.2(d + 15)2 − 11
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6. –/1 points ClarkIAlg2 4.3.010.MI. My Notes
Question Part
Points
Submissions Used
1
–/1
0/100
Total
–/1
 
Graph the data and the function on your calculator. Adjust a, h and/or k to get an eye-ball best fit. Answers will vary.
f(x) = −1.3(x − 3.1)2 + 17.6
x f(x)
0 −10.2
1 −1.9
2 3.8
3 7.0
4 7.5
5 5.4
f(x) =

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7. –/7 points ClarkIAlg2 4.3.022.MI. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6 7
–/1 –/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100 0/100
Total
–/7
 
The total revenue from selling water bottles is given in the table.
Price (dollars) Revenue (dollars)
7 1900
8 1940
9 1850
10 1600
11 1160
(a)
What variables are appropriate?
    
(b)
Find an equation for a model of these data. (Use the second set of values as the vertex and the fourth set of values as a point to calculate your equation.)
=
(c)
Give a reasonable domain and range for your model.
Domain:
    
Range:
    
(d)
Explain the meaning of the vertex for your model.
    
(e)
What does your model predict the revenue will be if they sell water bottles for $9.50? (Include units in your answer. More information.)
This model predicts the revenue will be about if the water bottles sell for $9.50 each.

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8. –/5 points ClarkIAlg2 4.3.038.MI. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5
–/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100
Total
–/5
 
Clark/Anfinson Pedagogical Focus
  • Students develop a quadratic model not in context.

Consider the following.
Input, x Output, y
−15 105.3
−12 29.7
−9 4.5
−6 29.7
−3 105.3
0 231.3
Find an equation for a model of the given data.
Explain why you decided to use the model type you selected.
A model fits the data best because the distribution shows the shape of a .
Give the domain and range for the model found. (Hint: This problem does not have a context, so the domain and range will not be restricted.)
Domain:
    
Range:
    

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9. –/6 points ClarkIAlg2 4.3.047. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 
Clark/Anfinson Pedagogical Focus
  • Students will create and compare linear and quadratic models for the same data set.

Find an equation for the requested model type of the given data.
The number of Hispanic families under the poverty threshold in the United States is given in the table.
Year Number of Families
(thousands)
2011 11,143
2012 11,358
2013 11,128
2014 10,853
2015 10,109
(a)
Find a linear model for these data, with
F(t)
 being the number of families, in thousands, under the poverty threshold
t
 years since 2010. (Use the first and last data points to calculate the slope and t-intercept.)
F(t) =
(b)
According to your linear model from part (a), how many Hispanic families were below the poverty threshold in 2009?
thousand families
(c)
Find a quadratic model for these data, with
F(t)
 being the number of families, in thousands, under the poverty threshold
t
 years since 2010. (Use the data from the year 2012 as the vertex and the data from the year 2011 to calculate the value of a.)
F(t) =
(d)
According to your quadratic model from part (c), how many Hispanic families were below the poverty threshold in 2009?
thousand families
(e)
In 2009 there were 10,345,000 Hispanic families below the poverty threshold. Which answer, from part (b) or part (d), is closer to the real number of Hispanic families below the poverty threshold in 2009?
    
(f)
Which model do you think fits the data better, the linear model or the quadratic model?
    
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10. –/6 points ClarkIAlg2 1.1.RQ.001. My Notes
Question Part
Points
Submissions Used
1 2 3 4 5 6
–/1 –/1 –/1 –/1 –/1 –/1
0/100 0/100 0/100 0/100 0/100 0/100
Total
–/6
 

  • Part 1

    How can I predict how long it will take me to travel a nature trail?
    Use some information about a path or trail that you have previously traveled to predict your rate of travel. Recall that distance traveled is equal to the product of the rate of travel and the time:
    d = rt.
    The values you enter in this part will be used to make later calculations.
    Consider a path or trail that you have traveled before.
    How long is this path in miles?
    mi
    How long, in hours, does it take you to travel this path from beginning to end?
    hr
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