Graph Using a Table of Values f(x)=-3(3)^(x+8)-5

$f (x) = - 3 {(3)}^{x + 8} - 5$

Step 1

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

$y = - 3 {(3)}^{(- 2) + 8} - 5$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{- 2 + 8} - 5$

Remove parentheses.

$y = - 3 {(3)}^{(- 2) + 8} - 5$

Simplify $- 3 {(3)}^{(- 2) + 8} - 5$ .

Simplify each term.

Add $- 2$ and $8$ .

$y = - 3 \cdot 3^{6} - 5$

Raise $3$ to the power of $6$ .

$y = - 3 \cdot 729 - 5$

Multiply $- 3$ by $729$ .

$y = - 2187 - 5$

Subtract $5$ from $- 2187$ .

$y = - 2192$

Step 3

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

$y = - 3 {(3)}^{(- 1) + 8} - 5$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{- 1 + 8} - 5$

Remove parentheses.

$y = - 3 {(3)}^{(- 1) + 8} - 5$

Simplify $- 3 {(3)}^{(- 1) + 8} - 5$ .

Simplify each term.

Add $- 1$ and $8$ .

$y = - 3 \cdot 3^{7} - 5$

Raise $3$ to the power of $7$ .

$y = - 3 \cdot 2187 - 5$

Multiply $- 3$ by $2187$ .

$y = - 6561 - 5$

Subtract $5$ from $- 6561$ .

$y = - 6566$

Step 5

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

$y = - 3 {(3)}^{(0) + 8} - 5$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{0 + 8} - 5$

Remove parentheses.

$y = - 3 {(3)}^{(0) + 8} - 5$

Simplify $- 3 {(3)}^{(0) + 8} - 5$ .

Simplify each term.

Add $0$ and $8$ .

$y = - 3 \cdot 3^{8} - 5$

Raise $3$ to the power of $8$ .

$y = - 3 \cdot 6561 - 5$

Multiply $- 3$ by $6561$ .

$y = - 19683 - 5$

Subtract $5$ from $- 19683$ .

$y = - 19688$

Step 7

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

$y = - 3 {(3)}^{(1) + 8} - 5$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{1 + 8} - 5$

Remove parentheses.

$y = - 3 {(3)}^{(1) + 8} - 5$

Simplify $- 3 {(3)}^{(1) + 8} - 5$ .

Simplify each term.

Add $1$ and $8$ .

$y = - 3 \cdot 3^{9} - 5$

Raise $3$ to the power of $9$ .

$y = - 3 \cdot 19683 - 5$

Multiply $- 3$ by $19683$ .

$y = - 59049 - 5$

Subtract $5$ from $- 59049$ .

$y = - 59054$

Step 9

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

$y = - 3 {(3)}^{(2) + 8} - 5$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{2 + 8} - 5$

Remove parentheses.

$y = - 3 {(3)}^{(2) + 8} - 5$

Simplify $- 3 {(3)}^{(2) + 8} - 5$ .

Simplify each term.

Add $2$ and $8$ .

$y = - 3 \cdot 3^{10} - 5$

Raise $3$ to the power of $10$ .

$y = - 3 \cdot 59049 - 5$

Multiply $- 3$ by $59049$ .

$y = - 177147 - 5$

Subtract $5$ from $- 177147$ .

$y = - 177152$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 2192 \\ - 1 & - 6566 \\ 0 & - 19688 \\ 1 & - 59054 \\ 2 & - 177152 \end{array}$

Step 12

Graph Using a Table of Values f(x)=-3(3)^(x+8)-5

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