# Given the function f(x)=-3-x, how do you express the value of (f(x+h)-f(x))/h?

May 6, 2018

$- 1$

#### Explanation:

$\frac{- 3 - \left(x + h\right) - \left(- 3 - x\right)}{h}$

$= \frac{\cancel{- 3} \cancel{- x} - h \cancel{+ 3} \cancel{+ x}}{h} = \frac{- h}{h} = - 1$

May 6, 2018

See explanation.

#### Explanation:

If $f \left(x\right) = - 3 - x$ then we can write that:

$f \left(x + h\right) = - 3 - \left(x + h\right) = - 3 - x - h$

$f \left(x\right) = - 3 - x$

Combining the two expressions we get:

$\frac{f \left(x + h\right) - f \left(x\right)}{h} = \frac{- 3 - x - h - \left(- 3 - x\right)}{h} =$

$\frac{- 3 - x - h + 3 + x}{h} = \frac{- h}{h} = - 1$