Finite Math Examples

$f (x) = x$ , $[- 4, 4]$

Step 1

The Intermediate Value Theorem states that, if $f$ is a real-valued continuous function on the interval $[a, b]$ , and $u$ is a number between $f (a)$ and $f (b)$ , then there is a $c$ contained in the interval $[a, b]$ such that $f (c) = u$ .

$u = f (c) = 0$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

Remove parentheses.

$f (- 4) = - 4$

Step 4

Remove parentheses.

$f (4) = 4$

Step 5

Rewrite the equation as $x = 0$ .

$x = 0$

Step 6

The Intermediate Value Theorem states that there is a root $f (c) = 0$ on the interval $[- 4, 4]$ because $f$ is a continuous function on $[- 4, 4]$ .

The roots on the interval $[- 4, 4]$ are located at $x = 0$ .

Step 7