Find @FORMULA f(x)=2x-3

$f (x) = 2 x - 3$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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

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

$f (x + h) = 2 (x + h) - 3$

Simplify the result.

Apply the distributive property.

$f (x + h) = 2 x + 2 h - 3$

The final answer is $2 x + 2 h - 3$ .

$2 x + 2 h - 3$

Reorder $2 x$ and $2 h$ .

$2 h + 2 x - 3$

Find the components of the definition.

$f (x + h) = 2 h + 2 x - 3$

$f (x) = 2 x - 3$

$f (x + h) = 2 h + 2 x - 3$

$f (x) = 2 x - 3$

Step 3

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{2 h + 2 x - 3 - (2 x - 3)}{h}$

Step 4

Simplify.

Simplify the numerator.

Apply the distributive property.

$\frac{2 h + 2 x - 3 - (2 x) - - 3}{h}$

Multiply $2$ by $- 1$ .

$\frac{2 h + 2 x - 3 - 2 x - - 3}{h}$

Multiply $- 1$ by $- 3$ .

$\frac{2 h + 2 x - 3 - 2 x + 3}{h}$

Subtract $2 x$ from $2 x$ .

$\frac{2 h + 0 - 3 + 3}{h}$

Add $2 h$ and $0$ .

$\frac{2 h - 3 + 3}{h}$

Add $- 3$ and $3$ .

$\frac{2 h + 0}{h}$

Add $2 h$ and $0$ .

$\frac{2 h}{h}$

Divide $2$ by $1$ .

$2$

Step 5