Expert: Sherry Wallin - 1/22/2009

Question
Determine the Difference Quotient where:
DQ=[g(x)-g(9)]/x-9

when: g(x)=(4/3)x-9

Answer
Hi Steven~
    I'm not certain what you mean by difference quotient. Is that what DQ is and if so is DQ multiplication notation? If they want you to evaluate a function then this is how you do it:

DQ = [(4/3)x-9-(4/3)*9-9]/(x-9)= [(4/3)x-9-12-9]/(x-9)=[(4/3)x-30]/(x-9)

or was it divide by x and then subtract 9?

You have DQ=[g(x)-g(9)]/x-9 which says to divide by x and then subtract 9 from everything else.

What I did was assume you really meant divide by (x-9). If it is the former then the answer is (4/3)-(30/x) - 9 = (-23/3)-(30/x).

I suspect what you are looking for is really
DQ = [(4/3)x-9-(4/3)*9-9]/(x-9)=[(4/3)x-9-12-9]/(x-9)=[(4/3)x-30]/(x-9)

Math Prof