If your solution to stated problem does not match the given solution, you should self-critique per instructions at http://vhcc2.vhcc.edu/dsmith/geninfo/labrynth_created_fall_05/levl1_22/levl2_81/file3_259.htm.

Your solution, attempt at solution. If you are unable to attempt a solution, give a phrase-by-phrase interpretation of the problem along with a statement of what you do or do not understand about it. This response should be given, based on the work you did in completing the assignment, before you look at the given solution.

009. `query 9

Question: `q **** Query problem 1.4.06 diff quotient for x^2-x+1 **** What is the simplified form of the difference quotient for x^2-x+1?

Your solution:

Confidence Rating:

Given Solution:

`a The difference quotient would be

[ f(x+`dx) - f(x) ] / `dx =

[ (x+`dx)^2 - (x+`dx) + 1 - (x^2 - x + 1) ] / `dx. Expanding the squared term, etc., this is

[ x^2 + 2 x `dx + `dx^2 - x - `dx + 1 - x^2 + x - 1 ] / `dx, which simplifies further to

}[ 2 x `dx - `dx + `dx^2 ] / `dx, then dividing by the `dx we get

2 x - 1 + `dx.

For x = 2 this simplifies to 2 * 2 - 1 + `dx = 3 + `dx. **

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Question: `q1.4.40 (was 1.4.34 f+g, f*g, f/g, f(g), g(f) for f=x/(x+1) and g=x^3

the requested functions and the domain and range of each.

Your solution:

Confidence Rating:

Given Solution:

`a (f+g)(x) = x / (x + 1) + x^3 = (x^4 + x^3 + x) / (x + 1). Domain: x can be any real number except -1.

(f * g)(x) = x^3 * x / (x+1) = x^4 / (x+1). Domain: x can be any real number except -1.

(f / g)(x) = [ x / (x+1) ] / x^3 = 1 / [x^2(x+1)] = 1 / (x^3 + x^2), Domain: x can be any real number except -1 or 0

f(g(x)) = g(x) / (g(x) + 1) = x^3 / (x^3 + 1). Domain: x can be any real number except -1

g(f(x)) = (f(x))^3 = (x / (x+1) )^3 = x^3 / (x+1)^3. Domain: x can be any real number except -1 **

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Question: `q 1.4.66 (was 1.4.60 graphs of |x|+3, -.5|x|, |x-2|, |x+1|-1, 2|x| from graph of |x|

Your solution:

Confidence Rating:

Given Solution:

`a The graph of y = | x | exists in quadrants 1 and 2 and has a 'v' shape with the point of the v at the origin.

It follows that:

The graph of | x |+3, which is shifted 3 units vertically from that of | x |, has a 'v' shape with the point of the v at (0,3).

The graph of -.5 | x |, which is stretched by factor -.5 relative to that of | x |, has an inverted 'v' shape with the point of the v at (0,0), with the 'v' extending downward and having half the (negative) slope of the graph of | x |.

The graph of | x-2 |, which is shifted 2 units horizontally from that of |x |, has a 'v' shape with the point of the v at (2, 0).

The graph of | x+1 |-1, which is shifted -1 unit vertically and -1 unit horizontally from that of | x |, has a 'v' shape with the point of the v at (-1, -1).

The graph of 2 |x |, which is stretched by factor 2 relative to that of | x |, has a 'v' shape with the point of the v at (0,0), with the 'v' extending upward and having double slope of the graph of | x |.

|x-2| shifts by +2 units because x has to be 2 greater to give you the same results for |x-2| as you got for |x|.

This also makes sense because if you make a table of y vs. x you find that the y values for |x| must be shifted +2 units in the positive direction to get the y values for |x-2|; this occurs for the same reason given above

For y = |x+1| - 1 the leftward 1-unit shift is because you need to use a lesser value of x to get the same thing for |x+1| that you got for |x|. The vertical -1 is because subtracting 1 shifts y downward by 1 unit **

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Question: `q1.4.71 (was 1.4.64 find x(p) from p(x) = 14.75/(1+.01x)

Your solution:

Confidence Rating:

Given Solution:

`a p = 14.75 / (1 + .01 x). Multiply both sides by 1 + .01 x to get

(1 + .01 x) * p = 14.75. Divide both sides by p to get

1 + .01 x = 14.75 / p. Subtract 1 from both sides to get

1 x = 14.75 / p - 1. Multiply both sides by 100 to get

= 1475 / p - 100. Put the right-hand side over common denominator p:

= (1475 - 100 p) / p.

If p = 10 then x = (1475 - 100 p) / p = (1475 - 100 * 10) / 10 = 475 / 10 = 47.5 **

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Question: `qWhat is the x as a function of p, and how many units are sold when the price is $10?

Your solution:

Confidence Rating:

Given Solution:

`a If p = 10 then x = (1475 - 100 p) / p = (1475 - 100 * 10) / 10 = 475 / 10 = 47.5 **

Self-critique (if necessary):

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