Graph Using a Table of Values g(x)=-(1/2)^x+3

$g (x) = - {(\frac{1}{2})}^{x} + 3$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Simplify $- {(\frac{1}{2})}^{- 2} + 3$ .

Simplify each term.

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

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

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

$y = - 1 \cdot 4 + 3$

Multiply $- 1$ by $4$ .

$y = - 4 + 3$

Add $- 4$ and $3$ .

$y = - 1$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Simplify $- {(\frac{1}{2})}^{- 1} + 3$ .

Simplify each term.

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

$y = - 1 \cdot 2 + 3$

Multiply $- 1$ by $2$ .

$y = - 2 + 3$

Add $- 2$ and $3$ .

$y = 1$

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

$y = - {(\frac{1}{2})}^{0} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = - {(\frac{1}{2})}^{0} + 3$

Simplify $- {(\frac{1}{2})}^{0} + 3$ .

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

$y = - \frac{1^{0}}{2^{0}} + 3$

Anything raised to $0$ is $1$ .

$y = - \frac{1}{2^{0}} + 3$

Anything raised to $0$ is $1$ .

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

Cancel the common factor of $1$ .

Cancel the common factor.

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

Rewrite the expression.

$y = - 1 \cdot 1 + 3$

Multiply $- 1$ by $1$ .

$y = - 1 + 3$

Add $- 1$ and $3$ .

$y = 2$

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

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

Solve the equation for $y$ .

Remove parentheses.

$y = - (\frac{1}{2}) + 3$

Simplify $- (\frac{1}{2}) + 3$ .

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{- 1 + 6}{2}$

Add $- 1$ and $6$ .

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Simplify $- {(\frac{1}{2})}^{2} + 3$ .

Simplify each term.

Apply the product rule to $\frac{1}{2}$ .

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

One to any power is one.

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

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

$y = - \frac{1}{4} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = - \frac{1}{4} + 3 \cdot \frac{4}{4}$

Combine $3$ and $\frac{4}{4}$ .

$y = - \frac{1}{4} + \frac{3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{- 1 + 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $3$ by $4$ .

$y = \frac{- 1 + 12}{4}$

Add $- 1$ and $12$ .

$y = \frac{11}{4}$

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

$\begin{array}{c} x & y \\ - 2 & - 1 \\ - 1 & 1 \\ 0 & 2 \\ 1 & \frac{5}{2} \\ 2 & \frac{11}{4} \end{array}$

Graph Using a Table of Values g(x)=-(1/2)^x+3

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