Graph Using a Table of Values f(x)=(5/4)^x

$f (x) = {(\frac{5}{4})}^{x}$

Step 1

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

$y = {(\frac{5}{4})}^{- 2}$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{5}{4})}^{- 2}$

Simplify ${(\frac{5}{4})}^{- 2}$ .

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

$y = {(\frac{4}{5})}^{2}$

Apply the product rule to $\frac{4}{5}$ .

$y = \frac{4^{2}}{5^{2}}$

Raise $4$ to the power of $2$ .

$y = \frac{16}{5^{2}}$

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

$y = \frac{16}{25}$

Step 3

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

$y = {(\frac{5}{4})}^{- 1}$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{5}{4})}^{- 1}$

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

$y = \frac{4}{5}$

Step 5

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

$y = {(\frac{5}{4})}^{0}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{5}{4})}^{0}$

Simplify ${(\frac{5}{4})}^{0}$ .

Apply the product rule to $\frac{5}{4}$ .

$y = \frac{5^{0}}{4^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{4^{0}}$

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 $y$ .

$y = {(\frac{5}{4})}^{1}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{5}{4}$

Remove parentheses.

$y = \frac{5}{4}$

Step 9

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

$y = {(\frac{5}{4})}^{2}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{5}{4})}^{2}$

Simplify ${(\frac{5}{4})}^{2}$ .

Apply the product rule to $\frac{5}{4}$ .

$y = \frac{5^{2}}{4^{2}}$

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

$y = \frac{25}{4^{2}}$

Raise $4$ to the power of $2$ .

$y = \frac{25}{16}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{16}{25} \\ - 1 & \frac{4}{5} \\ 0 & 1 \\ 1 & \frac{5}{4} \\ 2 & \frac{25}{16} \end{array}$

Step 12

Graph Using a Table of Values f(x)=(5/4)^x

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