Finite Math Examples

$(- 8, 1)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $1$ of the point, and set $x$ to the $x$ value $- 8$ of the point.

$1 = a^{- 8}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{- 8} = 1$ .

$a^{- 8} = 1$

Step 2.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{a^{8}} = 1$

Step 2.3

Find the LCD of the terms in the equation.

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Step 2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a^{8}, 1$

Step 2.3.2

The LCM of one and any expression is the expression.

$a^{8}$

Step 2.4

Multiply each term in $\frac{1}{a^{8}} = 1$ by $a^{8}$ to eliminate the fractions.

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Step 2.4.1

Multiply each term in $\frac{1}{a^{8}} = 1$ by $a^{8}$ .

$\frac{1}{a^{8}} a^{8} = 1 a^{8}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $a^{8}$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{1}{a^{8}} a^{8} = 1 a^{8}$

Step 2.4.2.1.2

Rewrite the expression.

$1 = 1 a^{8}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Multiply $a^{8}$ by $1$ .

$1 = a^{8}$

Step 2.5

Solve the equation.

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Step 2.5.1

Rewrite the equation as $a^{8} = 1$ .

$a^{8} = 1$

Step 2.5.2

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

$a = \pm \sqrt[8]{1}$

Step 2.5.3

Any root of $1$ is $1$ .

$a = \pm 1$

Step 2.5.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.5.4.1

First, use the positive value of the $\pm$ to find the first solution.

$a = 1$

Step 2.5.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$a = - 1$

Step 2.5.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$a = 1, - 1$

Step 3

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

$f (x) = {(1)}^{x}, f (x) = {(- 1)}^{x}$