Question

http://prntscr.com/bkj17g

I need help plugging in the missing variables. I know -9 goes into f(x) in the equation.

I got f(-9+0)-9/0

Answer 1

First , h is not 0 (they even show \( h \ne 0\) )
2nd, the expression should be
\[ \frac{f(x+h) - f(x)}{h} \]
and they tell you
f(x) = -9x

f( x+h) means "replace x in -9x with (x+h)"
in other words, in -9x
erase the x
-9___
and put in (x+h) instead:
-9(x+h)

f(x) means replace "x" in -9x with x
(of course, this has no effect, we get -9x)

Answer 2

Would putting -9 also work or does it have to be -9x

Answer 3

yes, the answer is -9


***Would putting -9 also work or does it have to be -9x***

I'm not sure what you are asking. If you have
f(x) = -9x

then the "string" f(x) means the same as the string -9x
or if you like
f(x) is the "name" for the rule: -9x
which means: multiply x by -9


f(2) would mean: replace x in the rule with 2: -9*2
and simplify: -18

f(y) would mean: replace x with y in the rule: -9x becomes -9y
(which can't be simplified)

f(x+h) means replace x with (x+h) in the rule: -9*(x+h)
which can also be written -9x -9h

Answer 4

the answer becomes
\[ \frac{f(x+h) - f(x)}{h} \\= \frac{-9x-9 h - (-9x)}{h} \\ =\frac{-9x -9h +9x}{h}\\
=\frac{-9h}{h} \\
=-9
\]