course Mth 163 bޫ~Ѻmassignment #005 005. Precalculus I 02-17-2008
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20:52:08 `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 --> f(-3)=(-3)^2=9 f(-20=(-2)^2=4 f(-1)=(-1)^2=1 f(0)=(0)^2=0 f(1)=(1)^2=1 f(2)=2^2=4 f(3)=3^2=9 confidence assessment: 2
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20:52:22 You should have obtained y values 9, 4, 1, 0, 1, 4, 9, in that order.
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RESPONSE --> ok self critique assessment: 3
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20:59:19 `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=0 y=2^1=2 y=2^2=4 y=2^3=8 confidence assessment: 2
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21:00:43 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 --> I missed the 2^0 but I see where it would be 1 instead of 0 because b^0=1 self critique assessment: 2
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21:05:20 `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 --> y=-3^-2=.1111 y=-2^-2=.25 y=-1^-2=1 y=0^-2=0 y=1^-2=1 y=2^-2=.25 y=3^-2=.1111 confidence assessment: 2
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21:07:23 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 --> So the 0^-2 would be an undefined instead of 0 self critique assessment: 2
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21:09:59 `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=-3^3=-27 y=-2^3=-8 y=-2^3=-1 y=0^3=0 y=1^3=1 y=2^3=8 y=3^3=27 confidence assessment: 3
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21:10:10 The y values should be -27, -8, -1, 0, 1, 4, 9.
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RESPONSE --> ok self critique assessment: 3
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21:23:31 `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 --> y=x^2 is a parabola that opens upward with it's vertex at (0,0) y=2^x is horizontal asymptote is the x axis y=x^-2 is a parabola that opens downward y=x^3 is a line that passes through (0,0) confidence assessment: 2
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21:26:08 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 believe that I did not graph one correctly. I showed that it was a horizontal asymptote to the x axis but the answer showed an asymptote to the y axis instead. I also did not describe the rates of increase etc. self critique assessment: 1
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21:35:26 `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 --> All of the y values are 3 more than they were for y=x^2 y=12,7,4,3,4,7,12 for y=x^2+3 y=9,4,1,0,1,4,9 for y=x^2 The graph were very similar they were both parabolas but the y=x^2+3 shift up the y axis by three units. confidence assessment: 3
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21:35:41 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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21:43:42 `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 y=x^3 y=-27,-8,-1,0,1,8,27 For y=(x-1)^3 y=-64,-27,-8,-1,0,1,8 confidence assessment: 1
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21:44:52 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 left off part of the answer they are all shifted 1 position to the right and the graphs of y=(x-1)^3 was also shifted 1 position to the right. self critique assessment: 2
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21:52:02 `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=.375,.75,1.5,0,6,12,24 y=.125,.25,.5,0,2,4,8 The origin for each remained at (0,0) but the remaining points all moved up three times there previous value. confidence assessment: 1
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21:52:21 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 --> ok self critique assessment: 3
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