course Mth 163 On question 4 I had a different value for the last two numbers. I just wanted to know where I made my error. My answers for y were 8 and 27, the qa answers were 4 and 9. Thanks assignment #005005.
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16:20:55 `questionNumber 50000 `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 --> y = -3^2=9 y = -2^2=4 y = -1^2=1 y = 0^2=0 y = 1^2=1 y = 2^2=4 y = 3^2=9 confidence assessment: 3
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16:21:04 `questionNumber 50000 You should have obtained y values 9, 4, 1, 0, 1, 4, 9, in that order.
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RESPONSE --> got it self critique assessment: 3
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16:22:36 `questionNumber 50000 `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 --> y = 2^-3=.125 y = 2^-2=.25 y = 2^-1=.5 y = 2^0=1 y = 2^1=2 y = 2^2=4 y = 2^3=8 confidence assessment: 3
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16:22:46 `questionNumber 50000 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 --> got it self critique assessment: 3
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16:23:47 `questionNumber 50000 `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 --> After plugging in the values I get .1111, .25, 1, 0 is undefined, 1, .25, .1111 in that order. confidence assessment: 2
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16:23:58 `questionNumber 50000 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 got it again self critique assessment: 2
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16:24:50 `questionNumber 50000 `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 --> After plugging in the values I got in this order -27, -8, -1, 0, 1, 8, 27 confidence assessment: 2
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16:25:23 `questionNumber 50000 The y values should be -27, -8, -1, 0, 1, 4, 9.
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RESPONSE --> !!!I don't uderstand where you got the 4 and 9!!! self critique assessment: 1
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16:26:56 `questionNumber 50000 `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 --> 1st graph is parabola with vertex pointed downward 2nd is curved line from quadrant two increasing steeply into quadrant one 3rd is parabola vertex pointed upward 4th is line extending from 3rd quadrant into first and increasing steeply. confidence assessment: 2
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16:27:04 `questionNumber 50000 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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RESPONSE --> i understand self critique assessment: 2
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16:28:11 `questionNumber 50000 `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 --> After making the table on paper I see that the y values are 3 higher than the values in y=x^2. The graph is also stretched 3 more. confidence assessment: 3
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16:28:20 `questionNumber 50000 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 --> I get this self critique assessment: 3
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16:30:02 `questionNumber 50000 `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 --> After making the table I see that if the x values are decreased by one then they are the same as the original x values in the x^3. The graph stretched one unit to the right. confidence assessment: 2
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16:30:15 `questionNumber 50000 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 --> I am still understanding self critique assessment: 2
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16:30:50 `questionNumber 50000 `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 value is 3 times greater than that of y=2^x. The graph would also be three times greater. confidence assessment: 2
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16:30:59 `questionNumber 50000 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 see. self critique assessment: 2
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