The difference quotient is given by:
[tex]\frac{f(x+h)-f(x)}{h}[/tex]Let's find it:
[tex]\begin{gathered} \frac{\lbrack-4(x+h)+5\rbrack-\lbrack-4x+5\rbrack}{h}=\frac{\lbrack-4x-4h+5\rbrack-\lbrack-4x+5\rbrack}{h} \\ =\frac{-4x-4h+5+4x-5}{h} \\ =\frac{-4h}{h} \\ =-4 \end{gathered}[/tex]Therefore, the difference quotient for the function given is -4
