Question

Find the difference quotient for each function and simplify.
f(x)=-2x+3

Answer 1

Recall that the difference quotient is given by \(\dfrac{f(x+h)-f(x)}{h}\). In this case, \(f(x) = -2x+3\) and thus \(f(x+h) = -2(x+h)+3\). Therefore, we see that $$\frac{f(x+h)-f(x)}{h} = \frac{-2(x+h)+3 - (-2x+3)}{h}=\ldots$$Can you take things from here? :-)

Answer 2

Just expand and simplify the numerator

Answer 3

so, f(x)=6

Answer 4

I don't get 6. How did you simplify \(\dfrac{-2(x+h)+3 - (-2x+3)}{h}\)?

Answer 5

-2x-2h+3+2-3

Answer 6

should be +2x at end so x's cancel which becomes -2h+6

Answer 7

You're missing something. The numerator expands out to \(-2x-2h+3+2x-3\), so the 2x terms cancel out like you said. But 3-3 = 0, so all that should be left over is -2h. Thus, \(\dfrac{-2(x+h)+3 - (-2x+3)}{h} = \dfrac{-2h}{h} = -2\).

Does this make sense? :-)

Answer 8

oh right, careless mistake with the +/-