Graph Using a Table of Values f(x)=(3/2)^(-x)

$f (x) = {(\frac{3}{2})}^{- x}$

Step 1

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

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

Step 2

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

Multiply $- 1$ by $- 2$ .

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

Apply the product rule to $\frac{3}{2}$ .

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

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

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

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

$y = \frac{9}{4}$

Step 3

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

$y = {(\frac{3}{2})}^{- (- 1)}$

Step 4

Simplify ${(\frac{3}{2})}^{- (- 1)}$ .

Multiply $- 1$ by $- 1$ .

$y = {(\frac{3}{2})}^{1}$

Simplify.

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

Step 5

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

$y = {(\frac{3}{2})}^{- (0)}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{2})}^{- (0)}$

Simplify ${(\frac{3}{2})}^{- (0)}$ .

Multiply $- 1$ by $0$ .

$y = {(\frac{3}{2})}^{0}$

Apply the product rule to $\frac{3}{2}$ .

$y = \frac{3^{0}}{2^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{2^{0}}$

Anything raised to $0$ is $1$ .

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

Divide $1$ by $1$ .

$y = 1$

Step 7

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

$y = {(\frac{3}{2})}^{- (1)}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{3}{2})}^{- (1)}$

Simplify ${(\frac{3}{2})}^{- (1)}$ .

Multiply $- 1$ by $1$ .

$y = {(\frac{3}{2})}^{- 1}$

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

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

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

Multiply $- 1$ by $2$ .

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

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

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

Apply the product rule to $\frac{2}{3}$ .

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

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

$y = \frac{4}{3^{2}}$

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

$y = \frac{4}{9}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{9}{4} \\ - 1 & \frac{3}{2} \\ 0 & 1 \\ 1 & \frac{2}{3} \\ 2 & \frac{4}{9} \end{array}$

Step 12

Graph Using a Table of Values f(x)=(3/2)^(-x)

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