Algebra Examples

$(5, 1)$

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 $5$ of the point.

$1 = a^{5}$

Step 2

Solve the equation for $a$ .

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Rewrite the equation as $a^{5} = 1$ .

$a^{5} = 1$

Take the 5th root of both sides of the equation to eliminate the exponent on the left side.

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

Any root of $1$ is $1$ .

$a = 1$

Step 3

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

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