course Mth 163 As long as you approve the location, can we take our first quiz sometime this week? Because it says that it's due after assigment 7?
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13:01:42 `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 Y values would be 9, 4, 1, 0, 1, 4, 9 confidence assessment: 2
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13:01:55 You should have obtained y values 9, 4, 1, 0, 1, 4, 9, in that order.
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RESPONSE --> Answered it correctly. self critique assessment: 3
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13:02:30 `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 values-1/8, 1/4, 1/2, 1, 2, 4 and 8 confidence assessment: 2
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13:03:02 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 --> OK! self critique assessment: 3
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13:04:18 `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 --> x values-1/9, 1/4, and 1 x= 0 is not defined. Other three values-1, 1/4, and 1/9 confidence assessment: 2
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13:04:48 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 --> A bit tricky, but i believe i came out with the correct answers. self critique assessment: 3
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13:05:11 `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 --> Y values would be -27, -8, -1, 0, 1, 4, 9 confidence assessment: 3
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13:05:26 The y values should be -27, -8, -1, 0, 1, 4, 9.
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RESPONSE --> Got this one correct. self critique assessment: 3
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13:08:37 `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 graph of y = x^2 --- the graph to the left of the y-axis is a mirror image of the graph to the right of the y-axis. y = 2^x----The graph intercepts the y-axis at y = 1. y = x^-2 -----is mirrored on the other side of the y-axis, so that the graph rises as we draw near the y-axis from either side. confidence assessment: 1
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13:09:54 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 was somewhat close to the descriptions. I wasn't exactly sure on this one. I just put in a few details rather than every single detail. Also, I forgot to describe the graph of y = x ^ 3. self critique assessment: 3
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13:11:43 `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 --> y = 12, 7, 4, 3, 4, 7, 12 y = x^2---- y = 9, 4, 1, 0, 1, 4, 9 confidence assessment: 2
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13:12:42 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: 3
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13:13:35 `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 --> values--64, -27, -8, -1, 0, 1, 8 vlues 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 close 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. confidence assessment: 3
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13:13:59 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 --> Got this one correct self critique assessment: 3
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13:15:26 `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 --> Y values---3/8, 3/4, 3/2, 3, 6, 12 and 24 The graph of y = 3 * 2^x has an overall shape close to that of y = 2^x, but each point lies 3 times farther from the x-axis. confidence assessment: 3
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13:15:37 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 --> correct. self critique assessment: 3
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