Finite Math Examples

y = 3^{x}

$y = 3^{x}$ ,

[- 3, 3]

$[- 3, 3]$

Step 1

The Intermediate Value Theorem states that, if

f

$f$ is a real-valued continuous function on the interval

[a, b]

$[a, b]$ , and

u

$u$ is a number between

f (a)

$f (a)$ and

f (b)

$f (b)$ , then there is a

c

$c$ contained in the interval

[a, b]

$[a, b]$ such that

f (c) = u

$f (c) = u$ .

u = f (c) = 0

$u = f (c) = 0$

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)

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Step 3

Calculate

$f (a) = f (- 3) = 3^{- 3}$ .

Tap for more steps...

Step 3.1

Rewrite the expression using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

$f (- 3) = \frac{1}{3^{3}}$

Step 3.2

Raise

$3$ to the power of

$3$ .

$f (- 3) = \frac{1}{27}$

Step 4

Raise

$3$ to the power of

$3$ .

$f (3) = 27$

Step 5

$0$ is not on the interval

$[\frac{1}{27}, 27]$ .

There is no root on the interval.

Step 6