Finite Math Examples

$(- 1, - 4)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $- 4$ of the point, and set $x$ to the $x$ value $- 1$ of the point.

$- 4 = a^{- 1}$

Step 2

Solve the equation for $a$ .

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Step 2.1

Rewrite the equation as $a^{- 1} = - 4$ .

$a^{- 1} = - 4$

Step 2.2

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

$\frac{1}{a} = - 4$

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.

$a, 1$

Step 2.3.2

The LCM of one and any expression is the expression.

$a$

Step 2.4

Multiply each term in $\frac{1}{a} = - 4$ by $a$ to eliminate the fractions.

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Step 2.4.1

Multiply each term in $\frac{1}{a} = - 4$ by $a$ .

$\frac{1}{a} a = - 4 a$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $a$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{1}{a} a = - 4 a$

Step 2.4.2.1.2

Rewrite the expression.

$1 = - 4 a$

Step 2.5

Solve the equation.

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Step 2.5.1

Rewrite the equation as $- 4 a = 1$ .

$- 4 a = 1$

Step 2.5.2

Divide each term in $- 4 a = 1$ by $- 4$ and simplify.

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Step 2.5.2.1

Divide each term in $- 4 a = 1$ by $- 4$ .

$\frac{- 4 a}{- 4} = \frac{1}{- 4}$

Step 2.5.2.2

Simplify the left side.

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Step 2.5.2.2.1

Cancel the common factor of $- 4$ .

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Step 2.5.2.2.1.1

Cancel the common factor.

$\frac{- 4 a}{- 4} = \frac{1}{- 4}$

Step 2.5.2.2.1.2

Divide $a$ by $1$ .

$a = \frac{1}{- 4}$

Step 2.5.2.3

Simplify the right side.

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Step 2.5.2.3.1

Move the negative in front of the fraction.

$a = - \frac{1}{4}$

Step 3

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

$f (x) = {(- \frac{1}{4})}^{x}$