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course mth 158
9/5 1:30
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:
goes through the x at (4/3, 0)
goes through the y at (0,-4)
confidence rating #$&*:
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2
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Question: `q002. Does the steepness of the graph in the preceding exercise (of the function y = 3x - 4) change? If so describe how it changes.
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Your solution:
The steepness of the graph does not change because the graph forms a straight line.
confidence rating #$&*:
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3
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Self-critique Rating:
ok
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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 is three
confidence rating #$&*:
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3
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Self-critique Rating:
ok
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Question: `q004. Make a table of y vs. x for y = x^2. Graph y = x^2 between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
The graph is increasing and the increase between the points is larger than the one behind it so it is increasing at an increasing rate.
confidence rating #$&*:
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3
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Self-critique Rating:
ok
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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:
The graph is decreasing and so is the steepness. The graph is decreasing at a decreasing rate.
confidence rating #$&*:
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3
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Self-critique Rating:
ok
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Question: `q006. Make a table of y vs. x for y = `sqrt(x). [note: `sqrt(x) means 'the square root of x']. Graph y = `sqrt(x) between x = 0 and x = 3.
Would you say that the graph is increasing or decreasing?
Does the steepness of the graph change and if so, how?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
The steepness of the graph is decreasing while the graph is increasing at a decreasing rate.
confidence rating #$&*:
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2
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Self-critique Rating:
ok
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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:
The graph is decreasing at a decreasing rate.
confidence rating #$&*:
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2
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Self-critique Rating:
ok
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Question: `q008. Suppose you stand still in front of a driveway. A car starts out next to you and moves away from you, traveling faster and faster.
If y represents the distance from you to the car and t represents the time in seconds since the car started out, would a graph of y vs. t be increasing or decreasing?
Would you say that the graph is increasing at an increasing rate, increasing at a constant rate, increasing at a decreasing rate, decreasing at an decreasing rate, decreasing at a constant rate, or decreasing at a decreasing rate?
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Your solution:
The graph would be increasing at an increasing rate because the distance of the car would become greater each second.
confidence rating #$&*:
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3
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Self-critique Rating:
ok"
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