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).