Graph Using a Table of Values y=5(1/2)^x-3

$y = 5 {(\frac{1}{2})}^{x} - 3$

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

$y = 5 {(\frac{1}{2})}^{- 2} - 3$

Solve the equation for $y$ .

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{- 2} - 3$

Simplify $5 {(\frac{1}{2})}^{- 2} - 3$ .

Simplify each term.

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

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

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

$y = 5 \cdot 4 - 3$

Multiply $5$ by $4$ .

$y = 20 - 3$

Subtract $3$ from $20$ .

$y = 17$

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

$y = 5 {(\frac{1}{2})}^{- 1} - 3$

Solve the equation for $y$ .

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{- 1} - 3$

Simplify $5 {(\frac{1}{2})}^{- 1} - 3$ .

Simplify each term.

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

$y = 5 \cdot 2 - 3$

Multiply $5$ by $2$ .

$y = 10 - 3$

Subtract $3$ from $10$ .

$y = 7$

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

$y = 5 {(\frac{1}{2})}^{0} - 3$

Solve the equation for $y$ .

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{0} - 3$

Simplify $5 {(\frac{1}{2})}^{0} - 3$ .

Simplify each term.

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

$y = 5 \frac{1^{0}}{2^{0}} - 3$

Anything raised to $0$ is $1$ .

$y = 5 \frac{1}{2^{0}} - 3$

Anything raised to $0$ is $1$ .

$y = 5 (\frac{1}{1}) - 3$

Cancel the common factor of $1$ .

Cancel the common factor.

$y = 5 (\frac{1}{1}) - 3$

Rewrite the expression.

$y = 5 \cdot 1 - 3$

Multiply $5$ by $1$ .

$y = 5 - 3$

Subtract $3$ from $5$ .

$y = 2$

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

$y = 5 {(\frac{1}{2})}^{1} - 3$

Solve the equation for $y$ .

Remove parentheses.

$y = 5 (\frac{1}{2}) - 3$

Simplify $5 (\frac{1}{2}) - 3$ .

Combine $5$ and $\frac{1}{2}$ .

$y = \frac{5}{2} - 3$

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

$y = \frac{5}{2} - 3 \cdot \frac{2}{2}$

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

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

Combine the numerators over the common denominator.

$y = \frac{5 - 3 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 3$ by $2$ .

$y = \frac{5 - 6}{2}$

Subtract $6$ from $5$ .

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

Move the negative in front of the fraction.

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

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

$y = 5 {(\frac{1}{2})}^{2} - 3$

Solve the equation for $y$ .

Remove parentheses.

$y = 5 {(\frac{1}{2})}^{2} - 3$

Simplify $5 {(\frac{1}{2})}^{2} - 3$ .

Simplify each term.

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

$y = 5 \frac{1^{2}}{2^{2}} - 3$

One to any power is one.

$y = 5 \frac{1}{2^{2}} - 3$

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

$y = 5 (\frac{1}{4}) - 3$

Combine $5$ and $\frac{1}{4}$ .

$y = \frac{5}{4} - 3$

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

$y = \frac{5}{4} - 3 \cdot \frac{4}{4}$

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

$y = \frac{5}{4} + \frac{- 3 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{5 - 3 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 3$ by $4$ .

$y = \frac{5 - 12}{4}$

Subtract $12$ from $5$ .

$y = \frac{- 7}{4}$

Move the negative in front of the fraction.

$y = - \frac{7}{4}$

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

$\begin{array}{c} x & y \\ - 2 & 17 \\ - 1 & 7 \\ 0 & 2 \\ 1 & - \frac{1}{2} \\ 2 & - \frac{7}{4} \end{array}$

Graph Using a Table of Values y=5(1/2)^x-3

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