Graph Using a Table of Values f(x)=-3(3)^x+7

$f (x) = - 3 {(3)}^{x} + 7$

Step 1

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

$y = - 3 {(3)}^{- 2} + 7$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{- 2} + 7$

Remove parentheses.

$y = - 3 {(3)}^{- 2} + 7$

Simplify $- 3 {(3)}^{- 2} + 7$ .

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - 3 \frac{1}{3^{2}} + 7$

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

$y = - 3 (\frac{1}{9}) + 7$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$y = 3 (- 1) \frac{1}{9} + 7$

Factor $3$ out of $9$ .

$y = 3 \cdot - 1 \frac{1}{3 \cdot 3} + 7$

Cancel the common factor.

$y = 3 \cdot - 1 \frac{1}{3 \cdot 3} + 7$

Rewrite the expression.

$y = - 1 (\frac{1}{3}) + 7$

Rewrite $- 1 (\frac{1}{3})$ as $- (\frac{1}{3})$ .

$y = - \frac{1}{3} + 7$

To write $7$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{1}{3} + 7 \cdot \frac{3}{3}$

Combine $7$ and $\frac{3}{3}$ .

$y = - \frac{1}{3} + \frac{7 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 1 + 7 \cdot 3}{3}$

Simplify the numerator.

Multiply $7$ by $3$ .

$y = \frac{- 1 + 21}{3}$

Add $- 1$ and $21$ .

$y = \frac{20}{3}$

Step 3

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

$y = - 3 {(3)}^{- 1} + 7$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{- 1} + 7$

Remove parentheses.

$y = - 3 {(3)}^{- 1} + 7$

Simplify $- 3 {(3)}^{- 1} + 7$ .

Simplify each term.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = - 3 (\frac{1}{3}) + 7$

Cancel the common factor of $3$ .

Factor $3$ out of $- 3$ .

$y = 3 (- 1) \frac{1}{3} + 7$

Cancel the common factor.

$y = 3 \cdot - 1 \frac{1}{3} + 7$

Rewrite the expression.

$y = - 1 + 7$

Add $- 1$ and $7$ .

$y = 6$

Step 5

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

$y = - 3 {(3)}^{0} + 7$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{0} + 7$

Remove parentheses.

$y = - 3 {(3)}^{0} + 7$

Simplify $- 3 {(3)}^{0} + 7$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = - 3 \cdot 1 + 7$

Multiply $- 3$ by $1$ .

$y = - 3 + 7$

Add $- 3$ and $7$ .

$y = 4$

Step 7

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

$y = - 3 {(3)}^{1} + 7$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3 + 7$

Remove parentheses.

$y = - 3 \cdot 3 + 7$

Simplify $- 3 \cdot 3 + 7$ .

Multiply $- 3$ by $3$ .

$y = - 9 + 7$

Add $- 9$ and $7$ .

$y = - 2$

Step 9

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

$y = - 3 {(3)}^{2} + 7$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = - 3 \cdot 3^{2} + 7$

Remove parentheses.

$y = - 3 {(3)}^{2} + 7$

Simplify $- 3 {(3)}^{2} + 7$ .

Simplify each term.

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

$y = - 3 \cdot 9 + 7$

Multiply $- 3$ by $9$ .

$y = - 27 + 7$

Add $- 27$ and $7$ .

$y = - 20$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{20}{3} \\ - 1 & 6 \\ 0 & 4 \\ 1 & - 2 \\ 2 & - 20 \end{array}$

Step 12

Graph Using a Table of Values f(x)=-3(3)^x+7

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