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Mth163

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can't take the log of a neg

logs can be negative, but you can't take the log of a negative.

If you think about what it would mean to take the log of a negative, you see that this would have to correspond to an exponential function with a negative value. There is no power p of b that makes b^p negative.

This isn't an easy line of reasoning, but you are capable of understanding it. Try to understand this as thoroughly as possible.

In order to take a log of negative that would mean to find the inverse your exponential function which would have to be negative exponential function , but that is not possible??? Because it would be imaginary???

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The value of an exponential function

y = b^x

is always positive, because if b is a positive number, b^x is always a positive number.

For example 2^x is always positive. For example 2^2 = 4, 2^3 = 8, 2^4 = 16, etc.. And 2^-2 = 1/4, 2^-3 = 1/8, 2^-4 = 1/16, etc...

No matter what the power, the result is positive.

To take the log of a negative you would have to have a negative value for the exponential function, which cannot be.

For example using base-10 logs,

log(-3) = x

would mean that

10^x = -3.

10^x is always positive, so there is no such x. That is, log(-3) is not defined and cannot be defined.
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Mth163

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receipt

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Mth163

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Test 1 complete

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I took test one today

July12,2013

Good.

I probably picked up tests yesterday around mid-afternoon, probably before you were done.

Email me Monday and I'll confirm receipt of your test.

I haven't been on my access page in awhile, what do you mean by Email me Monday and I'll confirm receipt of your test, (sorry if i did not email you by the way) I mean am i supposed to receive a 'receipt' after every test, that's just like a confirmation right???

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When I ask you to email me for confirmation, that means to send me an email so I can confirm to you that I have the test.

I do, in any case, have your test and the grade should be posted soon.
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Mth163

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What can a cubic polynomial do

Question: `qIt doesn't matter if you don't have a graphing utility--you can answer these questions based on what you know about the shape of each power function.

Why does a cubic polynomial, with is shape influenced by the y = x^3 power function, fit the first graph better than a quadratic or a linear polynomial?

What can a cubic polynomial do with this data that a quadratic can't?

YYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY

Your solution:

&&&

It has more curves

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It doesn't necessarily, but it can have more curves.

More specifically it can change directions twice, as would be necessary to pass through three zeros. (e.g., up through one, down through another, up through the last).
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confidence rating #$&*:: 2

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Given Solution:

`a** the concavity (i.e., the direction of curvature) of a cubic can change. Linear graphs don't curve, quadratic graphs

can be concave either upward or downward but not both on the same graph. Cubics can change concavity from upward

to downward. **

This says, more specifically, that the graph an increasing cubic will be increasing at a decreasing rate up to a point, the increasing at an increasing rate beyond that.

You should construct the graph of a decreasing cubic and think about how it would be described.

So you have more flexibility and movement with cubic functions because they can pretty much move to any point you need them

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@& When I ask you to email me for confirmation, that means to send me an email so I can confirm to you that I have the test. I do, in any case, have your test and the grade should be posted soon. *@

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@& It doesn't necessarily, but it can have more curves. More specifically it can change directions twice, as would be necessary to pass through three zeros. (e.g., up through one, down through another, up through the last). *@

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&#This looks good. See my notes. Let me know if you have any questions. &#

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When I ask you to email me for confirmation, that means to send me an email so I can confirm to you that I have the test.

I do, in any case, have your test and the grade should be posted soon.
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@&
It doesn't necessarily, but it can have more curves.

More specifically it can change directions twice, as would be necessary to pass through three zeros. (e.g., up through one, down through another, up through the last).
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