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course Math 158
August 30, 2010 @ 8:33pm. 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 email your work to the instructor. 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:
I constructed a table with two columns and labeled them x and y. I put the numbers 0,1,2, and 3 in the x column and then substituted these numbers for x in the equation y=3x-4 to find the y values. When substituting these numbers for x, the y values were -4, -1, 2, and 5. I then placed these numbers in the second column of the table labeled y. I then graphed these points on a set of x-y coordinate axes. Noting that these points lie on a straight line with a slope of 3. The points where the graph goes through the x and y axes is: When x = 0 then y = -4 (0.-4) When y =0, then x = 4/3 (4/3,0)
confidence rating #$&*
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3
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Question: `q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
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Your solution:
No, it has a constant slope of 3.
confidence rating #$&*
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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:
Rise/Run: 3
confidence rating #$&*
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3
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Question: `q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
When making a table for the equation y=x^2 when the numbers in the x column are 0,1,2,and 3 these make the y values in the right column 0,1,4, and 9. Therefore, when you graph these coordinates, it is increasing.
Yes, it gets steeper as the numbers get larger.
The graph increases at an increasing rate.
confidence rating #$&*
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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 an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
When making a table for the equation y=x^2 when the values for x column are -3,-2,-1, and 0, these numbers make the y values in the right column 9, 4, 1, and 0. Therefore, when you graph these coordinates, the line decreases.
Yes, the slope decreasing (flattens)as the numbers get smaller.
Yes it decreases at a decreasing rate.
confidence rating #$&*
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3
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Question: `q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
When making a table for the equation y=sqrt(x) with the values for x column being 0,1,2, and 3, the values for the y column are 0, 1, 2, 1.41 and 1.73. Therefore, when you graph these x-y coordinates, the line increases.
Yes, it increases as the numbers get larger.
It rate increases as the numbers get larger but the rate of change decreases.
confidence rating #$&*
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3
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Self-critique (if necessary):
Our solutions are different as the question advised that the x value for table and graph should be from 0 to 3 and my solution is the same as the given solution to this point. However, the given solution includes 0 to 4 and my solution does not include 4.
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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 an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
When making a table for y=5*2^(-x) when the values in the x column are 0, 1, 2, and 3, the y values will be: 5, 5/2, 5/4, and 5/8. These coordinates (0,5), (1,5/2), (2, 5/4), and (3, 5/8) shows that steepness of the graph does change. It decreases at a decreasing rate.
confidence rating #$&*
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3
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Question: `q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster.
If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
Since the car is moving away from you and is picking up speed as it moves, the graph showing the distance per time would be increasing at an increasing rate.
confidence rating #$&*
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3
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