qa 4

Your work has been received. Please scroll to the end of the document to see any inserted notes (in boldface) and a note at the end. The note at the end of the file will confirm that the file has been reviewed; be sure to read that note. If there is no note at the end, notify the instructor through the Submit Work form, and include the date of the posting to your access page.

.................................................

......!!!!!!!!...................................

11:37:22 `q001. Note that this assignment has 4 questions If f(x) = x^2 + 4, then find the values of the following: f(3), f(7) and f(-5). Plot the corresponding points on a graph of y = f(x) vs. x. Give a good description of your graph.

......!!!!!!!!...................................

RESPONSE --> f(x) = x^2 + 4 f(3) = 3^2 + 4 = 13 f(7) = 7^2 + 4 = 53 f(-5) = -5^2 + 4 = 14 it is a linear graph

.................................................

......!!!!!!!!...................................

11:38:06 f(x) = x^2 + 4. To find f(3) we replace x by 3 to obtain f(3) = 3^2 + 4 = 9 + 4 = 13. Similarly we have f(7) = 7^2 + 4 = 49 + 4 = 53 and f(-5) = (-5)^2 + 9 = 25 + 4 = 29. Graphing f(x) vs. x we will plot the points (3, 13), (7, 53), (-5, 29). The graph of f(x) vs. x will be a parabola passing through these points, since f(x) is seen to be a quadratic function, with a = 1, b = 0 and c = 4. The x coordinate of the vertex is seen to be -b/(2 a) = -0/(2*1) = 0. The y coordinate of the vertex will therefore be f(0) = 0 ^ 2 + 4 = 0 + 4 = 4. Moving along the graph one unit to the right or left of the vertex (0,4) we arrive at the points (1,5) and (-1,5) on the way to the three points we just graphed.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

11:38:19 `q002. If f(x) = x^2 + 4, then give the symbolic expression for each of the following: f(a), f(x+2), f(x+h), f(x+h)-f(x) and [ f(x+h) - f(x) ] / h. Expand and/or simplify these expressions as appropriate.

......!!!!!!!!...................................

RESPONSE --> I have no idea

.................................................

......!!!!!!!!...................................

11:39:07 If f(x) = x^2 + 4, then the expression f(a) is obtained by replacing x with a: f(a) = a^2 + 4. Similarly to find f(x+2) we replace x with x + 2: f(x+2) = (x + 2)^2 + 4, which we might expand to get (x^2 + 4 x + 4) + 4 or x^2 + 4 x + 8. To find f(x+h) we replace x with x + h to obtain f(x+h) = (x + h)^2 + 4 = x^2 + 2 h x + h^2 + 4. To find f(x+h) - f(x) we use the expressions we found for f(x) and f(x+h): f(x+h) - f(x) = [ x^2 + 2 h x + h^2 + 4 ] - [ x^2 + 4 ] = x^2 + 2 h x + 4 + h^2 - x^2 - 4 = 2 h x + h^2. To find [ f(x+h) - f(x) ] / h we can use the expressions we just obtained to see that [ f(x+h) - f(x) ] / h = [ x^2 + 2 h x + h^2 + 4 - ( x^2 + 4) ] / h = (2 h x + h^2) / h = 2 x + h.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

11:42:58 `q003. If f(x) = 5x + 7, then give the symbolic expression for each of the following: f(x1), f(x2), [ f(x2) - f(x1) ] / ( x2 - x1 ). Note that x1 and x2 stand for subscripted variables (x with subscript 1 and x with subscript 2), not for x * 1 and x * 2. x1 and x2 are simply names for two different values of x. If you aren't clear on what this means please ask the instructor.

......!!!!!!!!...................................

RESPONSE --> f(x) = 5x + 7 f(x1) = 5(x1) + 7 f(x2) = 5(x2) + 7 [f(x2) - f(x1)]/(x2-x1) = 5([f(x2)- f(x1)]/(x2-x1)

.................................................

......!!!!!!!!...................................

11:43:11 Replacing x by the specified quantities we obtain the following: f(x1) = 5 * x1 + 7, f(x2) = 5 * x2 + 7, [ f(x2) - f(x1) ] / ( x2 - x1) = [ 5 * x2 + 7 - ( 5 * x1 + 7) ] / ( x2 - x1) = [ 5 x2 + 7 - 5 x1 - 7 ] / (x2 - x1) = (5 x2 - 5 x1) / ( x2 - x1). We can factor 5 out of the numerator to obtain 5 ( x2 - x1 ) / ( x2 - x1 ) = 5.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

11:44:36 `q004. If f(x) = 5x + 7, then for what value of x is f(x) equal to -3?

......!!!!!!!!...................................

RESPONSE --> f(x) = 5x + 7 f(-3) = 5(-3) + 7 = -125 + 7 = -118

.................................................

......!!!!!!!!...................................

11:44:58 If f(x) is equal to -3 then we right f(x) = -3, which we translate into the equation 5x + 7 = -3. We easily solve this equation (subtract 7 from both sides then divide both sides by 5) to obtain x = -2.

......!!!!!!!!...................................

RESPONSE --> ok I did it wrong

.................................................

�ڦz�毳G����}���p������ Student Name: assignment #005

.................................................

......!!!!!!!!...................................

15:36:45 `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?

......!!!!!!!!...................................

RESPONSE --> the y values are 9, 4, 1, 0, 1, 4, 9

.................................................

......!!!!!!!!...................................

15:36:52 You should have obtained y values 9, 4, 1, 0, 1, 4, 9, in that order.

......!!!!!!!!...................................

RESPONSE --> right

.................................................

......!!!!!!!!...................................

15:38:23 `q002. Evaluate the function y = 2^x for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?

......!!!!!!!!...................................

RESPONSE --> the y values are: -8. 4. -2, 0, 2, 4, 8

.................................................

......!!!!!!!!...................................

15:38:42 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.

......!!!!!!!!...................................

RESPONSE --> ok I did the first three wrong

.................................................

......!!!!!!!!...................................

15:39:50 `q003. Evaluate the function y = x^-2 for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?

......!!!!!!!!...................................

RESPONSE --> the y values are: 9, 4, 2, 0, -2, -4, -9

.................................................

......!!!!!!!!...................................

15:40:20 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.

......!!!!!!!!...................................

RESPONSE --> ok I did those wrong by putting the formula together wrong

.................................................

......!!!!!!!!...................................

15:41:48 `q004. Evaluate the function y = x^3 for x values -3, -2, -1, 0, 1, 2, and 3. What are your y values?

......!!!!!!!!...................................

RESPONSE --> -1/18, -1/8. -1/3, 0, 1/3, 2/3, 1

.................................................

......!!!!!!!!...................................

15:42:03 The y values should be -27, -8, -1, 0, 1, 4, 9.

......!!!!!!!!...................................

RESPONSE --> ok I reversed the functions

.................................................

......!!!!!!!!...................................

15:42:52 `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.

......!!!!!!!!...................................

RESPONSE --> all the graphs are parabolas but all the vertexs are at different points

.................................................

......!!!!!!!!...................................

15:43:02 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.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

15:43:43 `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?

......!!!!!!!!...................................

RESPONSE --> they are plus 3 on each value and the graph is wider

.................................................

......!!!!!!!!...................................

15:43:48 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.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

15:44:23 `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.

......!!!!!!!!...................................

RESPONSE --> all the values are negative and the graphs are reversed

.................................................

......!!!!!!!!...................................

15:44:27 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.

......!!!!!!!!...................................

RESPONSE --> ok

.................................................

......!!!!!!!!...................................

15:45:11 `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.

......!!!!!!!!...................................

RESPONSE --> they are 3 times more and the graphs are wider

.................................................

......!!!!!!!!...................................

15:45:20 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.

......!!!!!!!!...................................

RESPONSE --> k

.................................................

"

Your answered most of these questions and appear to have an overall understanding of these ideas, but I would need to see more self-critique to see the degree of your understanding.

There were some errors in your responses that were not self-critiqued.