course Mth 163 ?????????V??assignment #005005.
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02:06:51 `q001. Note that this assignment has 8 questions Evaluate the function y = x^2 for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?
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RESPONSE --> The following would be a representation of the table I woud have for this problem: the x values are as follows - -3,-2,-1,0,1,2,3 also a note that these values are squared so the y values are as follows - -9,-4,-1,0,1,4,9. confidence assessment: 3
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02:07:27 You should have obtained y values 9, 4, 1, 0, 1, 4, 9, in that order.
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RESPONSE --> i understood this problem no critique necessary here. self critique assessment: 3
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02:13:49 `q002. Evaluate the function y = 2^x for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?
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RESPONSE --> The y values here are: -8,-4,-2,1,2,4,8. confidence assessment: 2
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02:16:52 By velocity exponents, b^-x = 1 / b^x. So for example 2^-2 = 1 / 2^2 = 1/4. Your y values will be 1/8, 1/4, 1/2, 1, 2, 4 and 8. Note that we have used the fact that for any b, b^0 = 1. It is a common error to say that 2^0 is 0. Note that this error would interfere with the pattern or progression of the y values.
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RESPONSE --> Since the first 3 numbers are negatives the exponents have to factored in differently. self critique assessment: 2
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02:24:35 `q003. Evaluate the function y = x^-2 for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?
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RESPONSE --> I'm not really sure of the answer here. So I think that the following values could be for y: -1/9,-1/4,-1,0,1,1/4,1/9. confidence assessment: 1
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02:25:53 By the laws of exponents, x^-p = 1 / x^p. So x^-2 = 1 / x^2, and your x values should be 1/9, 1/4, and 1. Since 1 / 0^2 = 1 / 0 and division by zero is not defined, the x = 0 value is undefined. The last three values will be 1, 1/4, and 1/9.
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RESPONSE --> I was not sure about the zero value here because this exercise is about exponential laws and how 0 should not be an answer here. self critique assessment: 2
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02:28:21 `q004. Evaluate the function y = x^3 for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?
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RESPONSE --> The y values are as follows: -1/27, -1/8,-1,0,1,8,27. confidence assessment: 3
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02:29:28 The y values should be -27, -8, -1, 0, 1, 4, 9.
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RESPONSE --> I thought the answers were wrong for the last three on the opposite page.?? self critique assessment: 2
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02:37:44 `q005. Sketch graphs for y = x^2, y = 2^x, y = x^-2 and y = x^3, using the values you obtained in the preceding four problems. Describe the graph of each function.
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RESPONSE --> The first graph of y=x^2 would be a straight line that slants left. I think that the second graph of y= 2^x would be a parabola that was very close and narrow facing up. The y= x^2 would be an uneven line that intersect in negative and positive numbers. confidence assessment: 1
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02:38:14 09-21-2008 02:38:14 The graph of y = x^2 is a parabola with its vertex at the origin. It is worth noting that the graph is symmetric with respect to the y-axis. That is, the graph to the left of the y-axis is a mirror image of the graph to the right of the y-axis. The graph of y = 2^x begins at x = -3 with value 1/8, which is relatively close to zero. The graph therefore starts to the left, close to the x-axis. With each succeeding unit of x, with x moving to the right, the y value doubles. This causes the graph to rise more and more quickly as we move from left to right. The graph intercepts the y-axis at y = 1. The graph of y = x^-2 rises more and more rapidly as we approach the y-axis from the left. It might not be clear from the values obtained here that this progression continues, with the y values increasing beyond bound, but this is the case. This behavior is mirrored on the other side of the y-axis, so that the graph rises as we approach the y-axis from either side. In fact the graph rises without bound as we approach the y-axis from either side. The y-axis is therefore a vertical asymptote for this graph. The graph of y = x ^ 3 has negative y values whenever x is negative and positive y values whenever x is positive. As we approach x = 0 from the left, through negative x values, the y values increase toward zero, but the rate of increase slows so that the graph actually levels off for an instant at the point (0,0) before beginning to increase again. To the right of x = 0 the graph increases faster and faster. Be sure to note whether your graph had all these characteristics, and whether your description included these characteristics. Note also any characteristics included in your description that were not included here.
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02:42:34 `q006. Make a table for y = x^2 + 3, using x values -3, -2, -1, 0, 1, 2, 3. How do the y values on the table compare to the y values on the table for y = x^2? How does the graph of y = x^2 + 3 compare to the graph of y = x^2?
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RESPONSE --> The y values would be as follows: -6,-1,2,3,4,7,12. The graph for this would be a parabola but unlike the graph for y= x^2, the points would be farther away from the origin of the graph. confidence assessment: 2
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02:43:46 A list of the y values will include, in order, y = 12, 7, 4, 3, 4, 7, 12. A list for y = x^2 would include, in order, y = 9, 4, 1, 0, 1, 4, 9. The values for y = x^2 + 3 are each 3 units greater than those for the function y = x^2. The graph of y = x^2 + 3 therefore lies 3 units higher at each point than the graph of y = x^2.
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RESPONSE --> ok self critique assessment: 1
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02:47:26 `q007. Make a table for y = (x -1)^3, using x values -3, -2, -1, 0, 1, 2, 3. How did the values on the table compare to the values on the table for y = x^3? Describe the relationship between the graph of y = (x -1)^3 and y = x^3.
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RESPONSE --> for the y values here, I got -64,-27,-8,-1,0,1,8. I assume that here the numbers are more spaced out and the graph is narrower from the vertex. confidence assessment: 1
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02:48:17 The values you obtained should have been -64, -27, -8, -1, 0, 1, 8. The values for y = x^3 are -27, -8, -1, 0, 1, 8, 27. The values of y = (x-1)^3 are shifted 1 position to the right relative to the values of y = x^3. The graph of y = (x-1)^3 is similarly shifted 1 unit to the right of the graph of y = x^3.
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RESPONSE --> The values have shifted away 1 unit due to the difference between the two equations that we graphed. self critique assessment: 2
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02:49:41 `q008. Make a table for y = 3 * 2^x, using x values -3, -2, -1, 0, 1, 2, 3. How do the values on the table compare to the values on the table for y = 2^x? Describe the relationship between the graph of y = 3 * 2^x and y = 2^x.
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RESPONSE --> The units here are 3 times more apart from the graph of y= 2^x. confidence assessment: 1
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02:50:58 You should have obtained y values 3/8, 3/4, 3/2, 3, 6, 12 and 24. Comparing these with the values 1/8, 1/4, 1/2, 1, 2, 4, 8 of the function y = 2^x we see that the values are each 3 times as great. The graph of y = 3 * 2^x has an overall shape similar to that of y = 2^x, but each point lies 3 times as far from the x-axis. It is also worth noting that at every point the graph of y = 3 * 2^x is three times as the past that of y = 2^x.
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RESPONSE --> I understood this equation and the greater or less units shows the difference between the two graphs regardless of what the equation represents. self critique assessment: 2
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