Graph Using a Table of Values f(x)=1/2*2^x-6

$f (x) = \frac{1}{2} \cdot 2^{x} - 6$

Step 1

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

$y = \frac{1}{2} \cdot 2^{- 2} - 6$

Step 2

Simplify $\frac{1}{2} \cdot 2^{- 2} - 6$ .

Simplify each term.

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

$y = \frac{1}{2} \cdot \frac{1}{2^{2}} - 6$

Combine.

$y = \frac{1 \cdot 1}{2 \cdot 2^{2}} - 6$

Multiply $2$ by $2^{2}$ by adding the exponents.

Multiply $2$ by $2^{2}$ .

Raise $2$ to the power of $1$ .

$y = \frac{1 \cdot 1}{2^{1} \cdot 2^{2}} - 6$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $2$ .

$y = \frac{1 \cdot 1}{2^{3}} - 6$

Multiply $1$ by $1$ .

$y = \frac{1}{2^{3}} - 6$

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

$y = \frac{1}{8} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = \frac{1}{8} - 6 \cdot \frac{8}{8}$

Combine $- 6$ and $\frac{8}{8}$ .

$y = \frac{1}{8} + \frac{- 6 \cdot 8}{8}$

Combine the numerators over the common denominator.

$y = \frac{1 - 6 \cdot 8}{8}$

Simplify the numerator.

Multiply $- 6$ by $8$ .

$y = \frac{1 - 48}{8}$

Subtract $48$ from $1$ .

$y = \frac{- 47}{8}$

Move the negative in front of the fraction.

$y = - \frac{47}{8}$

Step 3

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

$y = \frac{1}{2} \cdot 2^{- 1} - 6$

Step 4

Simplify $\frac{1}{2} \cdot 2^{- 1} - 6$ .

Simplify each term.

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

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

Multiply $\frac{1}{2} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{2}$ .

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

Multiply $2$ by $2$ .

$y = \frac{1}{4} - 6$

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{1}{4} - 6 \cdot \frac{4}{4}$

Combine $- 6$ and $\frac{4}{4}$ .

$y = \frac{1}{4} + \frac{- 6 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{1 - 6 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 6$ by $4$ .

$y = \frac{1 - 24}{4}$

Subtract $24$ from $1$ .

$y = \frac{- 23}{4}$

Move the negative in front of the fraction.

$y = - \frac{23}{4}$

Step 5

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

$y = \frac{1}{2} \cdot 2^{0} - 6$

Step 6

Simplify $\frac{1}{2} \cdot 2^{0} - 6$ .

Simplify each term.

Anything raised to $0$ is $1$ .

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

Multiply $\frac{1}{2}$ by $1$ .

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

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Combine $- 6$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $- 6$ by $2$ .

$y = \frac{1 - 12}{2}$

Subtract $12$ from $1$ .

$y = \frac{- 11}{2}$

Move the negative in front of the fraction.

$y = - \frac{11}{2}$

Step 7

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

$y = \frac{1}{2} \cdot 2^{1} - 6$

Step 8

Simplify $\frac{1}{2} \cdot 2^{1} - 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $2^{1}$ .

$y = \frac{1}{2} \cdot (2 \cdot 1) - 6$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 1) - 6$

Rewrite the expression.

$y = 1 - 6$

Subtract $6$ from $1$ .

$y = - 5$

Step 9

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

$y = \frac{1}{2} \cdot 2^{2} - 6$

Step 10

Simplify $\frac{1}{2} \cdot 2^{2} - 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $2^{2}$ .

$y = \frac{1}{2} \cdot (2 \cdot 2) - 6$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 2) - 6$

Rewrite the expression.

$y = 2 - 6$

Subtract $6$ from $2$ .

$y = - 4$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{47}{8} \\ - 1 & - \frac{23}{4} \\ 0 & - \frac{11}{2} \\ 1 & - 5 \\ 2 & - 4 \end{array}$

Step 12

Graph Using a Table of Values f(x)=1/2*2^x-6

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