Algebra Examples

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

Simplify the expression.

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Step 2.3.1.1

Add $- 2$ and $4$ .

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

Step 2.3.1.2

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

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

Step 2.3.1.3

One to any power is one.

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

Step 2.3.1.4

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

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

Step 2.3.2

Combine $- 3$ and $\frac{1}{4}$ .

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

Step 2.3.3

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Simplify the expression.

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Step 4.3.1.1

Add $- 1$ and $4$ .

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

Step 4.3.1.2

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

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

Step 4.3.1.3

One to any power is one.

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

Step 4.3.1.4

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

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

Step 4.3.2

Combine $- 3$ and $\frac{1}{8}$ .

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

Step 4.3.3

Move the negative in front of the fraction.

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

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

Step 6.2

Remove parentheses.

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

Step 6.3

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

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Step 6.3.1

Simplify the expression.

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Step 6.3.1.1

Add $0$ and $4$ .

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

Step 6.3.1.2

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

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

Step 6.3.1.3

One to any power is one.

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

Step 6.3.1.4

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

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

Step 6.3.2

Combine $- 3$ and $\frac{1}{16}$ .

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

Step 6.3.3

Move the negative in front of the fraction.

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

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Simplify the expression.

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Step 8.3.1.1

Add $1$ and $4$ .

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

Step 8.3.1.2

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

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

Step 8.3.1.3

One to any power is one.

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

Step 8.3.1.4

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

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

Step 8.3.2

Combine $- 3$ and $\frac{1}{32}$ .

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

Step 8.3.3

Move the negative in front of the fraction.

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Simplify the expression.

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Step 10.3.1.1

Add $2$ and $4$ .

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

Step 10.3.1.2

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

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

Step 10.3.1.3

One to any power is one.

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

Step 10.3.1.4

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

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

Step 10.3.2

Combine $- 3$ and $\frac{1}{64}$ .

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

Step 10.3.3

Move the negative in front of the fraction.

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

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{3}{4} \\ - 1 & - \frac{3}{8} \\ 0 & - \frac{3}{16} \\ 1 & - \frac{3}{32} \\ 2 & - \frac{3}{64} \end{array}$

Step 12