Graph Using a Table of Values f(x)=1/2(4)^x

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

Combine fractions.

Combine.

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

Multiply $1$ by $1$ .

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

Simplify the denominator.

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

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

Multiply the exponents in ${(2^{2})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Multiply $2$ by $2$ .

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

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

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

Add $1$ and $4$ .

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

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

$y = \frac{1}{32}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

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

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

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

Multiply $2$ by $4$ .

$y = \frac{1}{8}$

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

$y = \frac{1}{2} \cdot {(4)}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = \frac{1}{2} \cdot 4^{0}$

Remove parentheses.

$y = \frac{1}{2} \cdot {(4)}^{0}$

Simplify $\frac{1}{2} \cdot {(4)}^{0}$ .

Anything raised to $0$ is $1$ .

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

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

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

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = \frac{1}{2} \cdot (4)$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = \frac{1}{2} \cdot (2 (2))$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 2)$

Rewrite the expression.

$y = 2$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$y = \frac{1}{2} \cdot (2 (8))$

Cancel the common factor.

$y = \frac{1}{2} \cdot (2 \cdot 8)$

Rewrite the expression.

$y = 8$

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

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

Graph Using a Table of Values f(x)=1/2(4)^x

Related Questions

Support LCMGCF.com by disabling your adblocker.