Graph Using a Table of Values g(x)=3/4*2^x

$g (x) = \frac{3}{4} \cdot 2^{x}$

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

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

Simplify $\frac{3}{4} \cdot 2^{- 2}$ .

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

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

Combine fractions.

Combine.

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

Multiply $3$ by $1$ .

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

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

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

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

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

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

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

Simplify $\frac{3}{4} \cdot 2^{- 1}$ .

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

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

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

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

Multiply $4$ by $2$ .

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

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

$y = \frac{3}{4} \cdot 2^{0}$

Simplify $\frac{3}{4} \cdot 2^{0}$ .

Anything raised to $0$ is $1$ .

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

Multiply $\frac{3}{4}$ by $1$ .

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

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

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

Simplify $\frac{3}{4} \cdot 2^{1}$ .

Evaluate the exponent.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{3}{2 (2)} \cdot 2$

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify $\frac{3}{4} \cdot 2^{2}$ .

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3$

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

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

Graph Using a Table of Values g(x)=3/4*2^x

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