Graph Using a Table of Values f(x)=-(2/5)^(-x)

$f (x) = - {(\frac{2}{5})}^{- x}$

Step 1

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

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

Step 2

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

Multiply $- 1$ by $- 2$ .

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

Apply the product rule to $\frac{2}{5}$ .

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

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

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

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

$y = - \frac{4}{25}$

Step 3

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

$y = - {(\frac{2}{5})}^{- (- 1)}$

Step 4

Simplify $- {(\frac{2}{5})}^{- (- 1)}$ .

Multiply $- 1$ by $- 1$ .

$y = - {(\frac{2}{5})}^{1}$

Simplify.

$y = - \frac{2}{5}$

Step 5

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

$y = - {(\frac{2}{5})}^{- (0)}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - {(\frac{2}{5})}^{- (0)}$

Simplify $- {(\frac{2}{5})}^{- (0)}$ .

Simplify the expression.

Multiply $- 1$ by $0$ .

$y = - {(\frac{2}{5})}^{0}$

Apply the product rule to $\frac{2}{5}$ .

$y = - \frac{2^{0}}{5^{0}}$

Anything raised to $0$ is $1$ .

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

Anything raised to $0$ is $1$ .

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

Cancel the common factor of $1$ .

Cancel the common factor.

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

Rewrite the expression.

$y = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$y = - 1$

Step 7

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

$y = - {(\frac{2}{5})}^{- (1)}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - {(\frac{2}{5})}^{- (1)}$

Simplify $- {(\frac{2}{5})}^{- (1)}$ .

Multiply $- 1$ by $1$ .

$y = - {(\frac{2}{5})}^{- 1}$

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

$y = - \frac{5}{2}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

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

Multiply $- 1$ by $2$ .

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

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

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

Apply the product rule to $\frac{5}{2}$ .

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

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

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

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

$y = - \frac{25}{4}$

Step 11

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

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

Step 12

Graph Using a Table of Values f(x)=-(2/5)^(-x)

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