Question 160174: can someone please help me with this question;
Find and simplify the difference quotient f(x+h)-f(x) / h , h =(with slash through the = sign) 0 for the given function.
f(x) = 3x - 9
a. 3 + 6(x-9)/h
b. 0
c. 3
d. 3 + -18/h
Answer by gonzo(654)   (Show Source):
You can put this solution on YOUR website! i would say the answer is 3.
here's why
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f(x) = 3*x-9
if you want to find f(x+h) you simply replace all instances of x with x+h, so
f(x+h) = 3*(x+h)-9
your problem is to find and simplify the difference quotient (f(x+h) - f(x))/h
substituting 3*x-9 for f(x), and 3*(x+h)-9 for f(x+h), your difference quotient becomes (3*(x+h)-9 - (3*x-9))/h
multiplying out, this becomes (3*x + 3*h - 9 - (3*x - 9))/h
removing parentheses from (3*x - 9), this becomes
(3*x + 3*h - 9 - 3*x + 9)/h
you have to keep in mind the signs.
minus a plus is a minus.
minus a minus is a plus.
doing the additions and subtractions of like values, the equation becomes
3*h / h because +3*x and -3*x cancel out and +9 and -9 also cancel out.
dividing by h, the equation becomes 3*1 = 3.
the answer is 3 which would be c in your list of choices.
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