Find the Exponential Function (3,-7)

$(3, - 7)$

Step 1

To find an exponential function, $f (x) = a^{x}$ , containing the point, set $f (x)$ in the function to the $y$ value $- 7$ of the point, and set $x$ to the $x$ value $3$ of the point.

$- 7 = a^{3}$

Step 2

Solve the equation for $a$ .

Rewrite the equation as $a^{3} = - 7$ .

$a^{3} = - 7$

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

$a = \sqrt[3]{- 7}$

Simplify $\sqrt[3]{- 7}$ .

Rewrite $- 7$ as ${(- 1)}^{3} \cdot 7$ .

Rewrite $- 7$ as $- 1 (7)$ .

$a = \sqrt[3]{- 1 (7)}$

Rewrite $- 1$ as ${(- 1)}^{3}$ .

$a = \sqrt[3]{{(- 1)}^{3} \cdot 7}$

Pull terms out from under the radical.

$a = - 1 \sqrt[3]{7}$

Rewrite $- 1 \sqrt[3]{7}$ as $- \sqrt[3]{7}$ .

$a = - \sqrt[3]{7}$

Step 3

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

$f (x) = {(- \sqrt[3]{7})}^{x}$

Find the Exponential Function (3,-7)

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