Graph Using a Table of Values y=3*2^(x-2)+2

$y = 3 \cdot 2^{x - 2} + 2$

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

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

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

Simplify each term.

Subtract $2$ from $- 2$ .

$y = 3 \cdot 2^{- 4} + 2$

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

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

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

$y = 3 \cdot \frac{1}{16} + 2$

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

$y = \frac{3}{16} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$y = \frac{3}{16} + 2 \cdot \frac{16}{16}$

Combine $2$ and $\frac{16}{16}$ .

$y = \frac{3}{16} + \frac{2 \cdot 16}{16}$

Combine the numerators over the common denominator.

$y = \frac{3 + 2 \cdot 16}{16}$

Simplify the numerator.

Multiply $2$ by $16$ .

$y = \frac{3 + 32}{16}$

Add $3$ and $32$ .

$y = \frac{35}{16}$

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

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

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

Simplify each term.

Subtract $2$ from $- 1$ .

$y = 3 \cdot 2^{- 3} + 2$

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

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

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

$y = 3 \cdot \frac{1}{8} + 2$

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

$y = \frac{3}{8} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$y = \frac{3}{8} + 2 \cdot \frac{8}{8}$

Combine $2$ and $\frac{8}{8}$ .

$y = \frac{3}{8} + \frac{2 \cdot 8}{8}$

Combine the numerators over the common denominator.

$y = \frac{3 + 2 \cdot 8}{8}$

Simplify the numerator.

Multiply $2$ by $8$ .

$y = \frac{3 + 16}{8}$

Add $3$ and $16$ .

$y = \frac{19}{8}$

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

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

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

Simplify each term.

Subtract $2$ from $0$ .

$y = 3 \cdot 2^{- 2} + 2$

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

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

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

$y = 3 \cdot \frac{1}{4} + 2$

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

$y = \frac{3}{4} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{3}{4} + 2 \cdot \frac{4}{4}$

Combine $2$ and $\frac{4}{4}$ .

$y = \frac{3}{4} + \frac{2 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{3 + 2 \cdot 4}{4}$

Simplify the numerator.

Multiply $2$ by $4$ .

$y = \frac{3 + 8}{4}$

Add $3$ and $8$ .

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

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

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

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

Simplify each term.

Subtract $2$ from $1$ .

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

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

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

Combine $3$ and $\frac{1}{2}$ .

$y = \frac{3}{2} + 2$

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $2$ by $2$ .

$y = \frac{3 + 4}{2}$

Add $3$ and $4$ .

$y = \frac{7}{2}$

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

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

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

Simplify each term.

Subtract $2$ from $2$ .

$y = 3 \cdot 2^{0} + 2$

Anything raised to $0$ is $1$ .

$y = 3 \cdot 1 + 2$

Multiply $3$ by $1$ .

$y = 3 + 2$

Add $3$ and $2$ .

$y = 5$

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

$\begin{array}{c} x & y \\ - 2 & \frac{35}{16} \\ - 1 & \frac{19}{8} \\ 0 & \frac{11}{4} \\ 1 & \frac{7}{2} \\ 2 & 5 \end{array}$

Graph Using a Table of Values y=3*2^(x-2)+2

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