Algebra Examples

$y = 2^{x} - 3$

Step 1

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

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

Step 2

Simplify $2^{- 2} - 3$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 3$ by $4$ .

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

Step 2.5.2

Subtract $12$ from $1$ .

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

Step 2.6

Move the negative in front of the fraction.

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

Step 3

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

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

Step 4

Simplify $2^{- 1} - 3$ .

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Step 4.1

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

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $2$ .

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

Step 4.5.2

Subtract $6$ from $1$ .

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

Step 4.6

Move the negative in front of the fraction.

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

Step 5

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

$y = 2^{0} - 3$

Step 6

Simplify $2^{0} - 3$ .

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Step 6.1

Anything raised to $0$ is $1$ .

$y = 1 - 3$

Step 6.2

Subtract $3$ from $1$ .

$y = - 2$

Step 7

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

$y = 2^{1} - 3$

Step 8

Simplify $2^{1} - 3$ .

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Step 8.1

Evaluate the exponent.

$y = 2 - 3$

Step 8.2

Subtract $3$ from $2$ .

$y = - 1$

Step 9

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

$y = 2^{2} - 3$

Step 10

Simplify $2^{2} - 3$ .

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Step 10.1

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

$y = 4 - 3$

Step 10.2

Subtract $3$ from $4$ .

$y = 1$

Step 11

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

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

Step 12