Graph Using a Table of Values f(x)=(3/5)^x

$f (x) = {(\frac{3}{5})}^{x}$

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = {(\frac{3}{5})}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{5})}^{- 2}$

Simplify ${(\frac{3}{5})}^{- 2}$ .

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = {(\frac{5}{3})}^{2}$

Apply the product rule to $\frac{5}{3}$ .

$y = \frac{5^{2}}{3^{2}}$

Raise $5$ to the power of $2$ .

$y = \frac{25}{3^{2}}$

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

$y = \frac{25}{9}$

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = {(\frac{3}{5})}^{- 1}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{5})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = \frac{5}{3}$

Substitute $0$ for $x$ and find the result for $y$ .

$y = {(\frac{3}{5})}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{5})}^{0}$

Simplify ${(\frac{3}{5})}^{0}$ .

Apply the product rule to $\frac{3}{5}$ .

$y = \frac{3^{0}}{5^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{5^{0}}$

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1$

Substitute $1$ for $x$ and find the result for $y$ .

$y = {(\frac{3}{5})}^{1}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{3}{5}$

Remove parentheses.

$y = \frac{3}{5}$

Substitute $2$ for $x$ and find the result for $y$ .

$y = {(\frac{3}{5})}^{2}$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{5})}^{2}$

Simplify ${(\frac{3}{5})}^{2}$ .

Apply the product rule to $\frac{3}{5}$ .

$y = \frac{3^{2}}{5^{2}}$

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

$y = \frac{9}{5^{2}}$

Raise $5$ to the power of $2$ .

$y = \frac{9}{25}$

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{25}{9} \\ - 1 & \frac{5}{3} \\ 0 & 1 \\ 1 & \frac{3}{5} \\ 2 & \frac{9}{25} \end{array}$

Graph Using a Table of Values f(x)=(3/5)^x

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