Consider the given function,
[tex]f(x)=8x-9[/tex]
The difference quotient of a function is given by the formulal,
[tex]DQ=\frac{f(x+h)-f(x)}{h}[/tex]
Consider the following,
[tex]\begin{gathered} f(x+h)=8(x+h)-9 \\ f(x+h)=8x+8h-9 \end{gathered}[/tex]
Substitute the values in the formula,
[tex]\begin{gathered} DQ=\frac{(8x+8h-9)-(8x-9)}{h} \\ DQ=\frac{8x+8h-9-8x+9}{h} \\ DQ=\frac{8h}{h} \\ DQ=8 \end{gathered}[/tex]
Thus, the difference quotient for the given function is 8 units.
