Find the Difference Quotient f(x)=-3x+9

$f (x) = - 3 x + 9$

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Find the components of the definition.

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Evaluate the function at $x = x + h$ .

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Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = - 3 (x + h) + 9$

Simplify the result.

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Apply the distributive property.

$f (x + h) = - 3 x - 3 h + 9$

The final answer is $- 3 x - 3 h + 9$ .

$- 3 x - 3 h + 9$

Reorder $- 3 x$ and $- 3 h$ .

$- 3 h - 3 x + 9$

Find the components of the definition.

$f (x + h) = - 3 h - 3 x + 9$

$f (x) = - 3 x + 9$

$f (x + h) = - 3 h - 3 x + 9$

$f (x) = - 3 x + 9$

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{- 3 h - 3 x + 9 - (- 3 x + 9)}{h}$

Simplify.

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Simplify the numerator.

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Factor $3$ out of $- 3 x + 9$ .

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Factor $3$ out of $- 3 x$ .

$\frac{- 3 h - 3 x + 9 - (3 (- x) + 9)}{h}$

Factor $3$ out of $9$ .

$\frac{- 3 h - 3 x + 9 - (3 (- x) + 3 (3))}{h}$

Factor $3$ out of $3 (- x) + 3 (3)$ .

$\frac{- 3 h - 3 x + 9 - (3 (- x + 3))}{h}$

$\frac{- 3 h - 3 x + 9 - 1 \cdot 3 (- x + 3)}{h}$

Multiply $- 1$ by $3$ .

$\frac{- 3 h - 3 x + 9 - 3 (- x + 3)}{h}$

Factor $3$ out of $- 3 h - 3 x + 9 - 3 (- x + 3)$ .

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Factor $3$ out of $- 3 h$ .

$\frac{3 (- h) - 3 x + 9 - 3 (- x + 3)}{h}$

Factor $3$ out of $- 3 x$ .

$\frac{3 (- h) + 3 (- x) + 9 - 3 (- x + 3)}{h}$

Factor $3$ out of $9$ .

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

Factor $3$ out of $- 3 (- x + 3)$ .

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

Factor $3$ out of $3 (- h) + 3 (- x)$ .

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

Factor $3$ out of $3 (- h - x) + 3 (3)$ .

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

Factor $3$ out of $3 (- h - x + 3) + 3 (- (- x + 3))$ .

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

Apply the distributive property.

$\frac{3 (- h - x + 3 - - x - 1 \cdot 3)}{h}$

Multiply $- - x$ .

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Multiply $- 1$ by $- 1$ .

$\frac{3 (- h - x + 3 + 1 x - 1 \cdot 3)}{h}$

Multiply $x$ by $1$ .

$\frac{3 (- h - x + 3 + x - 1 \cdot 3)}{h}$

Multiply $- 1$ by $3$ .

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

Add $- x$ and $x$ .

$\frac{3 (- h + 0 + 3 - 3)}{h}$

Add $- h$ and $0$ .

$\frac{3 (- h + 3 - 3)}{h}$

Subtract $3$ from $3$ .

$\frac{3 (- h + 0)}{h}$

Add $- h$ and $0$ .

$\frac{3 \cdot - 1 h}{h}$

Combine exponents.

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Factor out negative.

$\frac{- (3 h)}{h}$

Multiply $3$ by $- 1$ .

$\frac{- 3 h}{h}$

Divide $- 3$ by $1$ .

$- 3$

Find the Difference Quotient f(x)=-3x+9

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