Precalculus Examples

$f (x) = x$ , $x = 0$

Consider the difference quotient formula. Use this formula to solve for the slope of the secant line $m_{s e c}$ .

$m_{s e c} = \frac{f (x + h) - f (x)}{h}$

Find the components of the definition.

Tap for more steps...

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

Tap for more steps...

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

$f (x + h) = (x + h)$

Simplify the result.

Tap for more steps...

Remove parentheses.

$f (x + h) = x + h$

The final answer is $x + h$ .

$x + h$

Find the components of the definition.

$f (x + h) = x + h$

$f (x) = x$

$f (x + h) = x + h$

$f (x) = x$

Plug in the components.

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

Simplify.

Tap for more steps...

Simplify the numerator.

Tap for more steps...

Multiply $- 1$ by $x$ to get $- x$ .

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

Subtract $x$ from $x$ to get $0$ .

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

Add $h$ and $0$ to get $h$ .

$\frac{h}{h}$

Reduce the expression by cancelling the common factors.

Tap for more steps...

Cancel the common factor.

$\frac{h}{h}$

Divide $1$ by $1$ to get $1$ .

$1$

Enter YOUR Problem