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course PHY 232
6/29
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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.
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Your solution:
To identify when the graph goes through the x-axis and the y-axis,
We plug in y=0 and x=0 in the equation respectively.
0=3x-4 y=3*0 - 4
3x=4 y=-4
X=4/3
These are the required values of x and y.
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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:
It is a straight line with, hence it has the same slope between two points. Hence the steepness of the graph remains the same throughout.
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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 is the rise/run between two points. Also we can write the equation of the line in its general form to find out the coefficient of x, which is the slope of the line.
Here the line is already written in its general form.
Hence the slope is 3.
`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?
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Your solution:
After making the graph for y=x^2 we can find out that it is increasing at an increasing rate between x=0 and x=3. After that too it goes increasing continuously. The steepness of the graph also changes in this interval. It becomes steeper and steeper between 0 and 3.
`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?
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Your solution:
In the interval x=-3 and x=0, the graph keeps on decreasing continuously. Also the graph keeps on getting less and less steeper as it goes from -3 to 0.
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?
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Your solution:
The graph is increasing in the interval x=0 to x=3.
The steepness of the graph changes and the graph becomes more and more steep as we go along.
The graph is increasing at an increasing rate.
`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 an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
Between x=0 and x=3, the graph decreases continuously. Hence it is decreasing at an decreasing rate. Also it becomes less and less steeper.
`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?
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Your solution:
The speed of the car increases so it goes further each second. On a graph of distance vs. clock time there would be a greater change in distance with each second, which would cause a greater slope with each subsequent second. The graph would therefore be increasing at an increasing rate
`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:
For graph of y = (x - 1)^2
It will be shifted slightly towards the right on the x-axis.
Hence it decreases at an decreasing rate till x=1 and then increases at an increasing rate at x=4 and after that too.
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`` 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.
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