Algebra Examples

$f (x) = - 2^{x + 5} - 3$

Step 1

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

$y = - 2^{(- 2) + 5} - 3$

Step 2

Simplify $- 2^{(- 2) + 5} - 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Add $- 2$ and $5$ .

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

Step 2.1.2

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

$y = - 1 \cdot 8 - 3$

Step 2.1.3

Multiply $- 1$ by $8$ .

$y = - 8 - 3$

Step 2.2

Subtract $3$ from $- 8$ .

$y = - 11$

Step 3

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

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

Step 4

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

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Step 4.1

Simplify each term.

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Step 4.1.1

Add $- 1$ and $5$ .

$y = - 2^{4} - 3$

Step 4.1.2

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

$y = - 1 \cdot 16 - 3$

Step 4.1.3

Multiply $- 1$ by $16$ .

$y = - 16 - 3$

Step 4.2

Subtract $3$ from $- 16$ .

$y = - 19$

Step 5

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

$y = - 2^{(0) + 5} - 3$

Step 6

Simplify $- 2^{(0) + 5} - 3$ .

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Step 6.1

Simplify each term.

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Step 6.1.1

Add $0$ and $5$ .

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

Step 6.1.2

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

$y = - 1 \cdot 32 - 3$

Step 6.1.3

Multiply $- 1$ by $32$ .

$y = - 32 - 3$

Step 6.2

Subtract $3$ from $- 32$ .

$y = - 35$

Step 7

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

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

Step 8

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

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Step 8.1

Simplify each term.

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Step 8.1.1

Add $1$ and $5$ .

$y = - 2^{6} - 3$

Step 8.1.2

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

$y = - 1 \cdot 64 - 3$

Step 8.1.3

Multiply $- 1$ by $64$ .

$y = - 64 - 3$

Step 8.2

Subtract $3$ from $- 64$ .

$y = - 67$

Step 9

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

$y = - 2^{(2) + 5} - 3$

Step 10

Simplify $- 2^{(2) + 5} - 3$ .

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Step 10.1

Simplify each term.

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Step 10.1.1

Add $2$ and $5$ .

$y = - 2^{7} - 3$

Step 10.1.2

Raise $2$ to the power of $7$ .

$y = - 1 \cdot 128 - 3$

Step 10.1.3

Multiply $- 1$ by $128$ .

$y = - 128 - 3$

Step 10.2

Subtract $3$ from $- 128$ .

$y = - 131$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - 11 \\ - 1 & - 19 \\ 0 & - 35 \\ 1 & - 67 \\ 2 & - 131 \end{array}$

Step 12