course Mth 271
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Question: `q001. 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:
x y
-3 -13
-2 -10
-1 -7
1 -1
2 2
3 5
x = 4/3 (4/3, 0)
y = -4(0, -4)
Confidence Assessment:
Great
Self-critique Rating:
To find the answers, I put the values for x into the equation to find y. To find the x and y intercepts, I solved for each respectively.
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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 slope of the graph remains the same.
Confidence Assessment:
Great
Self-critique Rating:
This is a logic question
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Question: `q003. What is the slope of the graph of the preceding two exercises (the function ia y = 3x - 4;slope is rise / run between two points of the graph)?
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Your solution:
(y-y)/(x-x)
(-10 + 13)/(-2 + 3) = 3
Confidence Assessment:
Great
Self-critique Rating:
To find the slope, chose two points on the line and put them into the slope equation.
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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:
x y
0 0
1 1
2 4
3 9
The graph is increasing at an increasing rate
Confidence Assessment:
Excellent
Self-critique Rating:
To find the solution, do the same thing as in the preceding problem.
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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:
x y
-3 9
-2 4
-1 1
0 0
The line is decreasing at a decreasing rate
Confidence Assessment:
Great
Self-critique Rating:
To solve this equation, follow the same steps as in the preceding question.
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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:
x y
0 0
1 1
2 1.41
3 1.73
The graph is increasing at a decreasing rate
Confidence Assessment:
Great
Self-critique Rating:
To solve this problem, follow the same steps as in the three preceding equations.
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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:
x y
0 5
1 2.5
2 1.25
3 .625
The graph is decreasing at a decreasing rate.
Confidence Assessment:
Great
Self-critique Rating:
To answer this problem, follow the steps in the 4 preceding equations.
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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:
Increasing at an increasing rate
Self-critique Rating:
By graphing the word problem, I can clearly see that the car is traveling faster the further it gets from me, meaning the line increases at an increasing rate.
&#Good responses. Let me know if you have questions. &#