Precalculus Examples

$f (x) = {(\frac{1}{3})}^{x}$

Step 1

Write $f (x) = {(\frac{1}{3})}^{x}$ as an equation.

$y = {(\frac{1}{3})}^{x}$

Step 2

Simplify ${(\frac{1}{3})}^{x}$ .

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Step 2.1

Apply the product rule to $\frac{1}{3}$ .

$y = \frac{1^{x}}{3^{x}}$

Step 2.2

One to any power is one.

$y = \frac{1}{3^{x}}$

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Simplify $\frac{1}{3^{0}}$ .

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Step 4.1.1

Anything raised to $0$ is $1$ .

$y = \frac{1}{1}$

Step 4.1.2

Divide $1$ by $1$ .

$y = 1$

Step 4.2

Use the $x$ and $y$ values to form the ordered pair.

$(0, 1)$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Evaluate the exponent.

$y = \frac{1}{3}$

Step 5.2

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{1}{3})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 6.1

Raise $3$ to the power of $2$ .

$y = \frac{1}{9}$

Step 6.2

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{1}{9})$

Step 7

These are three possible solutions to the equation.

$(0, 1), (1, \frac{1}{3}), (2, \frac{1}{9})$

Step 8