Algebra Examples

$f (x) = {(\frac{1}{2})}^{x + 4} - 3$

Step 1

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

$y = {(\frac{1}{2})}^{(- 2) + 4} - 3$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = {(\frac{1}{2})}^{- 2 + 4} - 3$

Step 2.2

Remove parentheses.

$y = {(\frac{1}{2})}^{(- 2) + 4} - 3$

Step 2.3

Simplify ${(\frac{1}{2})}^{(- 2) + 4} - 3$ .

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Add $- 2$ and $4$ .

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

Step 2.3.1.2

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

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

Step 2.3.1.3

One to any power is one.

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

Step 2.3.1.4

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

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

Step 2.3.2

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

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

Step 2.3.3

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

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

Step 2.3.4

Combine the numerators over the common denominator.

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

Step 2.3.5

Simplify the numerator.

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Step 2.3.5.1

Multiply $- 3$ by $4$ .

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

Step 2.3.5.2

Subtract $12$ from $1$ .

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

Step 2.3.6

Move the negative in front of the fraction.

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

Step 3

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

$y = {(\frac{1}{2})}^{(- 1) + 4} - 3$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = {(\frac{1}{2})}^{- 1 + 4} - 3$

Step 4.2

Remove parentheses.

$y = {(\frac{1}{2})}^{(- 1) + 4} - 3$

Step 4.3

Simplify ${(\frac{1}{2})}^{(- 1) + 4} - 3$ .

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Add $- 1$ and $4$ .

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

Step 4.3.1.2

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

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

Step 4.3.1.3

One to any power is one.

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

Step 4.3.1.4

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

$y = \frac{1}{8} - 3$

Step 4.3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = \frac{1}{8} - 3 \cdot \frac{8}{8}$

Step 4.3.3

Combine $- 3$ and $\frac{8}{8}$ .

$y = \frac{1}{8} + \frac{- 3 \cdot 8}{8}$

Step 4.3.4

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 8}{8}$

Step 4.3.5

Simplify the numerator.

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Step 4.3.5.1

Multiply $- 3$ by $8$ .

$y = \frac{1 - 24}{8}$

Step 4.3.5.2

Subtract $24$ from $1$ .

$y = \frac{- 23}{8}$

Step 4.3.6

Move the negative in front of the fraction.

$y = - \frac{23}{8}$

Step 5

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

$y = {(\frac{1}{2})}^{(0) + 4} - 3$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = {(\frac{1}{2})}^{0 + 4} - 3$

Step 6.2

Remove parentheses.

$y = {(\frac{1}{2})}^{(0) + 4} - 3$

Step 6.3

Simplify ${(\frac{1}{2})}^{(0) + 4} - 3$ .

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Add $0$ and $4$ .

$y = {(\frac{1}{2})}^{4} - 3$

Step 6.3.1.2

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

$y = \frac{1^{4}}{2^{4}} - 3$

Step 6.3.1.3

One to any power is one.

$y = \frac{1}{2^{4}} - 3$

Step 6.3.1.4

Raise $2$ to the power of $4$ .

$y = \frac{1}{16} - 3$

Step 6.3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$y = \frac{1}{16} - 3 \cdot \frac{16}{16}$

Step 6.3.3

Combine $- 3$ and $\frac{16}{16}$ .

$y = \frac{1}{16} + \frac{- 3 \cdot 16}{16}$

Step 6.3.4

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 16}{16}$

Step 6.3.5

Simplify the numerator.

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Step 6.3.5.1

Multiply $- 3$ by $16$ .

$y = \frac{1 - 48}{16}$

Step 6.3.5.2

Subtract $48$ from $1$ .

$y = \frac{- 47}{16}$

Step 6.3.6

Move the negative in front of the fraction.

$y = - \frac{47}{16}$

Step 7

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

$y = {(\frac{1}{2})}^{(1) + 4} - 3$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = {(\frac{1}{2})}^{1 + 4} - 3$

Step 8.2

Remove parentheses.

$y = {(\frac{1}{2})}^{(1) + 4} - 3$

Step 8.3

Simplify ${(\frac{1}{2})}^{(1) + 4} - 3$ .

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

Add $1$ and $4$ .

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

Step 8.3.1.2

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

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

Step 8.3.1.3

One to any power is one.

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

Step 8.3.1.4

Raise $2$ to the power of $5$ .

$y = \frac{1}{32} - 3$

Step 8.3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$y = \frac{1}{32} - 3 \cdot \frac{32}{32}$

Step 8.3.3

Combine $- 3$ and $\frac{32}{32}$ .

$y = \frac{1}{32} + \frac{- 3 \cdot 32}{32}$

Step 8.3.4

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 32}{32}$

Step 8.3.5

Simplify the numerator.

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Step 8.3.5.1

Multiply $- 3$ by $32$ .

$y = \frac{1 - 96}{32}$

Step 8.3.5.2

Subtract $96$ from $1$ .

$y = \frac{- 95}{32}$

Step 8.3.6

Move the negative in front of the fraction.

$y = - \frac{95}{32}$

Step 9

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

$y = {(\frac{1}{2})}^{(2) + 4} - 3$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = {(\frac{1}{2})}^{2 + 4} - 3$

Step 10.2

Remove parentheses.

$y = {(\frac{1}{2})}^{(2) + 4} - 3$

Step 10.3

Simplify ${(\frac{1}{2})}^{(2) + 4} - 3$ .

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Step 10.3.1

Simplify each term.

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Step 10.3.1.1

Add $2$ and $4$ .

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

Step 10.3.1.2

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

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

Step 10.3.1.3

One to any power is one.

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

Step 10.3.1.4

Raise $2$ to the power of $6$ .

$y = \frac{1}{64} - 3$

Step 10.3.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{64}{64}$ .

$y = \frac{1}{64} - 3 \cdot \frac{64}{64}$

Step 10.3.3

Combine $- 3$ and $\frac{64}{64}$ .

$y = \frac{1}{64} + \frac{- 3 \cdot 64}{64}$

Step 10.3.4

Combine the numerators over the common denominator.

$y = \frac{1 - 3 \cdot 64}{64}$

Step 10.3.5

Simplify the numerator.

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Step 10.3.5.1

Multiply $- 3$ by $64$ .

$y = \frac{1 - 192}{64}$

Step 10.3.5.2

Subtract $192$ from $1$ .

$y = \frac{- 191}{64}$

Step 10.3.6

Move the negative in front of the fraction.

$y = - \frac{191}{64}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{11}{4} \\ - 1 & - \frac{23}{8} \\ 0 & - \frac{47}{16} \\ 1 & - \frac{95}{32} \\ 2 & - \frac{191}{64} \end{array}$

Step 12