Finite Math Examples

$(5, - 5)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $- 5$ of the point, and set $x$ to the $x$ value $5$ of the point.

$- 5 = a^{5}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{5} = - 5$ .

$a^{5} = - 5$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[5]{- 5}$

Step 2.3

Simplify $\sqrt[5]{- 5}$ .

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Step 2.3.1

Rewrite $- 5$ as ${(- 1)}^{5} \cdot 5$ .

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Step 2.3.1.1

Rewrite $- 5$ as $- 1 (5)$ .

$a = \sqrt[5]{- 1 (5)}$

Step 2.3.1.2

Rewrite $- 1$ as ${(- 1)}^{5}$ .

$a = \sqrt[5]{{(- 1)}^{5} \cdot 5}$

Step 2.3.2

Pull terms out from under the radical.

$a = - 1 \sqrt[5]{5}$

Step 2.3.3

Rewrite $- 1 \sqrt[5]{5}$ as $- \sqrt[5]{5}$ .

$a = - \sqrt[5]{5}$

Step 3

Substitute each value for $a$ back into the function $f (x) = a^{x}$ to find each possible exponential function.

$f (x) = {(- \sqrt[5]{5})}^{x}$