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Topic: Pre-calc
Replies: 2   Last Post: Sep 8, 2004 7:27 PM

 Messages: [ Previous | Next ]
 Yogi Posts: 323 Registered: 12/6/04
Re: Pre-calc
Posted: Sep 8, 2004 12:10 PM

On 8 Sep 04 09:32:15 -0400 (EDT), jeremy wrote:
>I haven't taken math since high scool and I forgot everything, can
>someone please explain this problem for me.(Difference quotient)
>
>f(x)= 2x+5

The only statement of the problem is the two words "Difference
quotient"! The difference quotient for a function f(x) is the
fraction (quotient) formed of the difference (f(x)- f(a))/(x-a) or
sometimes (f(b)-f(a))/(b-a). Unfortunately, you have given us neither
a nor b!

For this particular example, it doesn't matter. Since this is a
"linear function", the difference quotient for any a, b (or any a, x)
is a constant: the slope.

Taking a to be any number, f(a)= 2a+ 5. Taking b to be any number,
f(b)= 2b+ 4. f(b)- f(a)= (2b+5)- (2a+ 5)= (2b-2a)+ (5-5)=
2(b-a). That's the numerator of the difference quotient. The
denomiator is b-a so: (f(b)- f(a))/(b-a)= 2(b-a)/(b-a)= 2 (as long as
b is not equal to a).

Date Subject Author
9/8/04 jeremy
9/8/04 Yogi
9/8/04 Stan Brown