#$&*
course MTH 173
9/8 130am
Describing Graphs: introduces students to a rudimentary vocabulary for describing graphs a basic vocabulary for describing some important aspects of graphs. Copy and paste this document into a text editor, insert your responses and submit using the Submit_Work_Form.If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
002. Describing Graphs
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Question: `q001. You will frequently need to describe the graphs you have constructed in this course. This exercise is designed to get you used to some of the terminology we use to describe graphs. Please complete this exercise and submit your work as instructed.
Note that you should do these graphs on paper without using a calculator. None of the arithmetic involved here should require a calculator, and you should not require the graphing capabilities of your calculator to answer these questions.
Problem 1. We make a table for y = 2x + 7 as follows: We construct two columns, and label the first column 'x' and the second 'y'. Put the numbers -3, -2, -1, -, 1, 2, 3 in the 'x' column. We substitute -3 into the expression and get y = 2(-3) + 7 = 1. We substitute -2 and get y = 2(-2) + 7 = 3. Substituting the remaining numbers we get y values 5, 7, 9, 11 and 13. These numbers go into the second column, each next to the x value from which it was obtained. We then graph these points on a set of x-y coordinate axes. Noting that these points lie on a straight line, we then construct the line through the points.
Now make a table for and graph the function y = 3x - 4.
Identify the intercepts of the graph, i.e., the points where the graph goes through the x and the y axes.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
(-4,0), (-3,1), (-2,3), (-1,5), (1,9), (2,11), (3,13), (4,15)
It intercepts the y axis at 0, 7 and the x axis at -4, 0
@&
You don't appear to have made a table for y = 3 x - 4, which is what was requested.
The discussion of y = 2 x + 7 was an example.
However note that the points (-4, 0) is not on the graph of this function. When x = -4, you get y = -1, not 0.
*@
confidence rating #$&*: 2
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Self-critique (if necessary): My answer does not match the given solution and I don’t understand how the fraction 4/3 is on the x axis. There isn’t much of a solution to show that so I don’t understand what I did wrong #########
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Self-critique Rating:
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Question: `q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When graphing this on paper with numbers plugged in I did not get the same answer as plugging it in on my calculator. The calculator showed a straight line while my sheet showed a change in steepness. The given answer from you is a straight line with no steepness. I’m not sure how my answers are different.
confidence rating #$&*: 2
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): Do not understand how my answers are different
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Self-critique Rating:
*********************************************
Question: `q003. What is the slope of the graph of the preceding two exercises (the function is y = 3x - 4;slope is rise / run between two points of the graph)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: For my x coordinates I chose 2 and 4. So I plug those into the equation and get (2,2) and (4,8). I found used a search engine to refresh my memory on rise and run. I found them both, rise=6, run=2. You subtract the y variables to get the rise and the x variables to get the run. When you divide the two, you get slope which is equal to 3 in this equation
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary):
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Self-critique Rating: 3
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Question: `q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: when the equation is solved with the given x values, we get (0,0), (1,1), (2,4), and (3,9)
When graphed, the values are increasing at an increasing rate. There is a jump from 1,1 to 2,4, and then another huge jump to 3,9. It is not constant because it is not gradual
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary):
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q005. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = -3 and x = 0.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
When the table is made, we get the values (-3,9), (-2,4), (-1,1), and (0,0).
When graphed, the points are causing the graph to decrease. The steepness of the graph changes by going downwards towards the x axis instead of expanding up towards the y. Since it isn’t huge gaps between the points and it isn’t at a constant rate, the graph is decreasing at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary):
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When a table is made, I used the x values 0,1,2,3
I got the points (0,0), (1,1), (2,1.4), and (3,1.7) From what I could tell at this point the graph was increasing slowly. The y values don’t change that much, instead they stay decimals of 1. I speculate this will cause the graph to decrease less and less. Once I graphed it, I saw my guess was right. The graph increases but at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): I had to refresh myself on square roots and how to work them on a calculator. I still can’t remember how to do it by hand. Unlike the other problems, it was easier to work this problem all at once instead of in steps but I’m happy I came out with the correct answers.
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q007. Make a table of y vs. x for y = 5 * 2^(-x). Graph y = 5 * 2^(-x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at a decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: As I plug the values 1,2,3 into a table to get the y values, I get (1,2.5), (2,1.25, and (3,.625). As I graph these I see that the graph is decreasing. The steepness changes because the intervals aren’t as spread apart as they started out being. Even though the x values are increasing, the y values are decreasing and since they are decreasing at such a slow rate, this graph is also decreasing at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): I first worked the equation wrong. I looked at the given solution and remembered the a^(-b)=1/(a^b) trick and reworked my equation using that.
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster.
If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Even though I don’t understand a d vs t graph, I would say that since the speed of the car increases it causes it to go further with time. Since the distance is increasing with time, there would be an increase of the slope. An increasing graph at an increasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique (if necessary): See solution about not fully knowing what to use in a d vs t graph
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Self-critique Rating: 3
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Question: `q009. As you saw above, on the interval from x = -3 to x = 3 the graph of y = x^2 is decreasing at a decreasing rate up to x = 0 and increasing at an increasing rate beyond x = 0.
How would you describe the behavior of the graph of y = (x - 1)^2 between x = -3 and x = 3?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: In the table, I got the points (-3,16), (-2,9), (-1,4), (0,1), (1,0), (2,1), (3,4)
I observed that the graph decreases at a decreasing rate until 1,0 and then it begins to change direction and increase at an increasing rate. The points make a v shaped pattern on the graph.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
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Self-critique Rating: Nothing to critique it to
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
@&
You have apparently eliminated the given solutions. Many of your questions reference the given solution, so the posted document won't be much good to you without that information.
*@
@&
`` Please take a few minutes and copy your responses into a complete copy of the document, and resubmit. Among other things, it is important that your portfolio page (i.e., your access page) contain all the information of the original.
*@
#$&*
course MTH 173
9/8 130am
Describing Graphs: introduces students to a rudimentary vocabulary for describing graphs a basic vocabulary for describing some important aspects of graphs. Copy and paste this document into a text editor, insert your responses and submit using the Submit_Work_Form.If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm
Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.
002. Describing Graphs
*********************************************
Question: `q001. You will frequently need to describe the graphs you have constructed in this course. This exercise is designed to get you used to some of the terminology we use to describe graphs. Please complete this exercise and submit your work as instructed.
Note that you should do these graphs on paper without using a calculator. None of the arithmetic involved here should require a calculator, and you should not require the graphing capabilities of your calculator to answer these questions.
Problem 1. We make a table for y = 2x + 7 as follows: We construct two columns, and label the first column 'x' and the second 'y'. Put the numbers -3, -2, -1, -, 1, 2, 3 in the 'x' column. We substitute -3 into the expression and get y = 2(-3) + 7 = 1. We substitute -2 and get y = 2(-2) + 7 = 3. Substituting the remaining numbers we get y values 5, 7, 9, 11 and 13. These numbers go into the second column, each next to the x value from which it was obtained. We then graph these points on a set of x-y coordinate axes. Noting that these points lie on a straight line, we then construct the line through the points.
Now make a table for and graph the function y = 3x - 4.
Identify the intercepts of the graph, i.e., the points where the graph goes through the x and the y axes.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
(-4,0), (-3,1), (-2,3), (-1,5), (1,9), (2,11), (3,13), (4,15)
It intercepts the y axis at 0, 7 and the x axis at -4, 0
@&
You don't appear to have made a table for y = 3 x - 4, which is what was requested.
The discussion of y = 2 x + 7 was an example.
However note that the points (-4, 0) is not on the graph of this function. When x = -4, you get y = -1, not 0.
*@
confidence rating #$&*: 2
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): My answer does not match the given solution and I don’t understand how the fraction 4/3 is on the x axis. There isn’t much of a solution to show that so I don’t understand what I did wrong #########
------------------------------------------------
Self-critique Rating:
*********************************************
Question: `q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When graphing this on paper with numbers plugged in I did not get the same answer as plugging it in on my calculator. The calculator showed a straight line while my sheet showed a change in steepness. The given answer from you is a straight line with no steepness. I’m not sure how my answers are different.
confidence rating #$&*: 2
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): Do not understand how my answers are different
------------------------------------------------
Self-critique Rating:
*********************************************
Question: `q003. What is the slope of the graph of the preceding two exercises (the function is y = 3x - 4;slope is rise / run between two points of the graph)?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: For my x coordinates I chose 2 and 4. So I plug those into the equation and get (2,2) and (4,8). I found used a search engine to refresh my memory on rise and run. I found them both, rise=6, run=2. You subtract the y variables to get the rise and the x variables to get the run. When you divide the two, you get slope which is equal to 3 in this equation
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: when the equation is solved with the given x values, we get (0,0), (1,1), (2,4), and (3,9)
When graphed, the values are increasing at an increasing rate. There is a jump from 1,1 to 2,4, and then another huge jump to 3,9. It is not constant because it is not gradual
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q005. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = -3 and x = 0.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
When the table is made, we get the values (-3,9), (-2,4), (-1,1), and (0,0).
When graphed, the points are causing the graph to decrease. The steepness of the graph changes by going downwards towards the x axis instead of expanding up towards the y. Since it isn’t huge gaps between the points and it isn’t at a constant rate, the graph is decreasing at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary):
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: When a table is made, I used the x values 0,1,2,3
I got the points (0,0), (1,1), (2,1.4), and (3,1.7) From what I could tell at this point the graph was increasing slowly. The y values don’t change that much, instead they stay decimals of 1. I speculate this will cause the graph to decrease less and less. Once I graphed it, I saw my guess was right. The graph increases but at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): I had to refresh myself on square roots and how to work them on a calculator. I still can’t remember how to do it by hand. Unlike the other problems, it was easier to work this problem all at once instead of in steps but I’m happy I came out with the correct answers.
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q007. Make a table of y vs. x for y = 5 * 2^(-x). Graph y = 5 * 2^(-x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at a decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: As I plug the values 1,2,3 into a table to get the y values, I get (1,2.5), (2,1.25, and (3,.625). As I graph these I see that the graph is decreasing. The steepness changes because the intervals aren’t as spread apart as they started out being. Even though the x values are increasing, the y values are decreasing and since they are decreasing at such a slow rate, this graph is also decreasing at a decreasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): I first worked the equation wrong. I looked at the given solution and remembered the a^(-b)=1/(a^b) trick and reworked my equation using that.
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster.
If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution:
Even though I don’t understand a d vs t graph, I would say that since the speed of the car increases it causes it to go further with time. Since the distance is increasing with time, there would be an increase of the slope. An increasing graph at an increasing rate.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
Self-critique (if necessary): See solution about not fully knowing what to use in a d vs t graph
------------------------------------------------
Self-critique Rating: 3
*********************************************
Question: `q009. As you saw above, on the interval from x = -3 to x = 3 the graph of y = x^2 is decreasing at a decreasing rate up to x = 0 and increasing at an increasing rate beyond x = 0.
How would you describe the behavior of the graph of y = (x - 1)^2 between x = -3 and x = 3?
YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
Your solution: In the table, I got the points (-3,16), (-2,9), (-1,4), (0,1), (1,0), (2,1), (3,4)
I observed that the graph decreases at a decreasing rate until 1,0 and then it begins to change direction and increase at an increasing rate. The points make a v shaped pattern on the graph.
confidence rating #$&*: 3
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
------------------------------------------------
Self-critique Rating: Nothing to critique it to
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
"
Self-critique (if necessary):
------------------------------------------------
Self-critique rating:
#*&!
@&
You have apparently eliminated the given solutions. Many of your questions reference the given solution, so the posted document won't be much good to you without that information.
*@
@&
`` Please take a few minutes and copy your responses into a complete copy of the document, and resubmit. Among other things, it is important that your portfolio page (i.e., your access page) contain all the information of the original.
*@