Odd Function Problem  TOPIC_SOLVED

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Odd Function Problem

Postby burnbird16 on Sun Aug 22, 2010 9:58 pm

Yet another problem for your brilliant minds to ponder!

Simplify (f(x+h) - f(x))/h, where f(x) = 2x+3

Here's what I did, please tell me if I made an error.

2(x+h) +3 - 2x - 3 / h

2x + 2h + 3 - 2x - 3 /h

2h/h

2

Thank you for your help!
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 10:40 pm

burnbird16 wrote:Yet another problem for your brilliant minds to ponder!

Simplify (f(x+h) - f(x))/h, where f(x) = 2x+3

Here's what I did, please tell me if I made an error.

2(x+h) +3 - 2x - 3 / h

2x + 2h + 3 - 2x - 3 /h

2h/h

2

Thank you for your help!


You really need to use parentheses or do this...






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Re: Odd Function Problem

Postby burnbird16 on Sun Aug 22, 2010 10:43 pm

I'm sorry, but I don't know how to do what you just did.
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 10:44 pm

burnbird16 wrote:I'm sorry, but I don't know how to do what you just did.










Code: Select all
[tex]\frac{2(x+h) +3 - (2x + 3)} { h}[/tex]

[tex]\frac{2x+2h +3 - 2x - 3} { h}[/tex]

[tex]\frac{2h} { h}=2[/tex]
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 10:46 pm

you could have also did it this way...

[2(x+h) +3 - 2x - 3] / h

=[2x + 2h + 3 - 2x - 3]/h

=2h/h

=2

for h not equal to zero
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Re: Odd Function Problem

Postby burnbird16 on Sun Aug 22, 2010 10:49 pm

Ok, thank you. :) So was I correct,then? If so, I have a few more I would like for you to look at, if you have time.
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 10:51 pm

burnbird16 wrote:Ok, thank you. :) So was I correct,then? If so, I have a few more I would like for you to look at, if you have time.


Your final answer is correct but your notation is not. Your really need to put in brackets or parentheses.
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 10:55 pm

burnbird16 wrote:... I have a few more I would like for you to look at, if you have time.


I'll be on for a little while...and I'm sure there are others here that can also help with this.
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Re: Odd Function Problem

Postby burnbird16 on Sun Aug 22, 2010 11:03 pm

Of course, and I will do so, thank you very much ^^

However, I do have a few more problems that I need some help with.

I'll just list them off, as I don't even know how to start any of them.

30. a) The graph of a quadratic function has x-intercepts, -1 and 3, and a range consisting of all numbers less than or equal to 4. Determine an expression for the function. (I tried to reverse factor, but I got a positive parabola, not a negative one.)

31. Write as a single equation in x and y: x = t + 1, y =

34. Express x in terms of the other variables in this picture: http://www.flickr.com/photos/46210274@N07/4918073428/ (I drew it myself, I know it's kind of small, but it is a replica of the drawings in the packet)
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Re: Odd Function Problem

Postby Martingale on Sun Aug 22, 2010 11:10 pm

burnbird16 wrote:...
30. a) The graph of a quadratic function has x-intercepts, -1 and 3, and a range consisting of all numbers less than or equal to 4. Determine an expression for the function. (I tried to reverse factor, but I got a positive parabola, not a negative one.)
...



for this your function needs to look like...




since you want the range to be less than or equal to 4 we know the parabola goes down so

by symmetry the max will occur at x=1 (the middle of -1 and 3)

so plug 1 into the function and solve for k (ie solve )
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