Graph Using a Table of Values f(x)=3^(x-2)-7

$f (x) = 3^{x - 2} - 7$

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

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

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

Simplify each term.

Subtract $2$ from $- 2$ .

$y = 3^{- 4} - 7$

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

$y = \frac{1}{3^{4}} - 7$

Raise $3$ to the power of $4$ .

$y = \frac{1}{81} - 7$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{81}{81}$ .

$y = \frac{1}{81} - 7 \cdot \frac{81}{81}$

Combine $- 7$ and $\frac{81}{81}$ .

$y = \frac{1}{81} + \frac{- 7 \cdot 81}{81}$

Combine the numerators over the common denominator.

$y = \frac{1 - 7 \cdot 81}{81}$

Simplify the numerator.

Multiply $- 7$ by $81$ .

$y = \frac{1 - 567}{81}$

Subtract $567$ from $1$ .

$y = \frac{- 566}{81}$

Move the negative in front of the fraction.

$y = - \frac{566}{81}$

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

$y = 3^{(- 1) - 2} - 7$

Simplify $3^{(- 1) - 2} - 7$ .

Simplify each term.

Subtract $2$ from $- 1$ .

$y = 3^{- 3} - 7$

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

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

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

$y = \frac{1}{27} - 7$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$y = \frac{1}{27} - 7 \cdot \frac{27}{27}$

Combine $- 7$ and $\frac{27}{27}$ .

$y = \frac{1}{27} + \frac{- 7 \cdot 27}{27}$

Combine the numerators over the common denominator.

$y = \frac{1 - 7 \cdot 27}{27}$

Simplify the numerator.

Multiply $- 7$ by $27$ .

$y = \frac{1 - 189}{27}$

Subtract $189$ from $1$ .

$y = \frac{- 188}{27}$

Move the negative in front of the fraction.

$y = - \frac{188}{27}$

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

$y = 3^{(0) - 2} - 7$

Simplify $3^{(0) - 2} - 7$ .

Simplify each term.

Subtract $2$ from $0$ .

$y = 3^{- 2} - 7$

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

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

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

$y = \frac{1}{9} - 7$

To write $- 7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{1}{9} - 7 \cdot \frac{9}{9}$

Combine $- 7$ and $\frac{9}{9}$ .

$y = \frac{1}{9} + \frac{- 7 \cdot 9}{9}$

Combine the numerators over the common denominator.

$y = \frac{1 - 7 \cdot 9}{9}$

Simplify the numerator.

Multiply $- 7$ by $9$ .

$y = \frac{1 - 63}{9}$

Subtract $63$ from $1$ .

$y = \frac{- 62}{9}$

Move the negative in front of the fraction.

$y = - \frac{62}{9}$

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

$y = 3^{(1) - 2} - 7$

Simplify $3^{(1) - 2} - 7$ .

Simplify each term.

Subtract $2$ from $1$ .

$y = 3^{- 1} - 7$

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

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

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 $3$ .

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

Subtract $21$ from $1$ .

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

Move the negative in front of the fraction.

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

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

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

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

Simplify each term.

Subtract $2$ from $2$ .

$y = 3^{0} - 7$

Anything raised to $0$ is $1$ .

$y = 1 - 7$

Subtract $7$ from $1$ .

$y = - 6$

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

$\begin{array}{c} x & y \\ - 2 & - \frac{566}{81} \\ - 1 & - \frac{188}{27} \\ 0 & - \frac{62}{9} \\ 1 & - \frac{20}{3} \\ 2 & - 6 \end{array}$

Graph Using a Table of Values f(x)=3^(x-2)-7

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