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course Phy 241
06/06/2013 10:22 pm
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.
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Your solution: The intercept of the graph for y = 3x - 4 are (0, -4).
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Self-critique Rating: 3
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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.
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Your solution: The graph creates a straight line without any change of steepness.
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Self-critique Rating: 3
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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)?
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Your solution: The slope of the graph of the function is 3.
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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 and decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
x y
0 0
1 1
2 4
3 9
According to the y units, the graph is increasing as it moves from left to right.
The steepness does change in which the line is increasing in an increasing rate.
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Self-critique Rating: 3
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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 and decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
x y
-3 9
-2 4
-1 1
0 0
The graph is decreasing in a slower pace and as for the steepness of the graph is decreasing as well.
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Self-critique Rating: 3
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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 and decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
x y
0 0
1 1
2 1.414
3 1.732
4 2
Based on the y-units, the graph would be increasing at a decreasing rate since the steepness of the same graph is decreasing.
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Self-critique Rating: 3
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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 and decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Self-critique Rating: 3
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Your solution:
x y
0 5
1 2.5
2 1.25
3 0.625
The y values are decrease but in a slower rate each time. This means that the graph is decreasing at a decreasing rate.
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Self-critique Rating: 3
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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 and decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
The graph would increase because the car will increase its speed and move each second. The graph displays a big increasing slope because huge change in distance with each second, which in turn the graph is increasing in an increasing rate.
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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?
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Your solution:
x y
-3 16
-2 9
-1 4
0 1
1 0
2 1
3 4
The graph will be in a form of parabola in which the line will produce a U like shape.
Self-critique Rating: 3
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