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Yogi
Posts:
323
Registered:
12/6/04
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Re: Pre-calc
Posted:
Sep 8, 2004 12:10 PM
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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).
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