Graph Using a Table of Values f(x)=4*(2/3)^x+1

$f (x) = 4 \cdot {(\frac{2}{3})}^{x} + 1$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Apply the product rule to $\frac{3}{2}$ .

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

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

$y = 4 \cdot \frac{9}{2^{2}} + 1$

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

$y = 4 \cdot \frac{9}{4} + 1$

Cancel the common factor of $4$ .

Cancel the common factor.

$y = 4 \cdot \frac{9}{4} + 1$

Rewrite the expression.

$y = 9 + 1$

Add $9$ and $1$ .

$y = 10$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 2 \cdot 3 + 1$

Multiply $2$ by $3$ .

$y = 6 + 1$

Add $6$ and $1$ .

$y = 7$

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

$y = 4 \cdot {(\frac{2}{3})}^{0} + 1$

Solve the equation for $y$ .

Remove parentheses.

$y = 4 \cdot {(\frac{2}{3})}^{0} + 1$

Simplify $4 \cdot {(\frac{2}{3})}^{0} + 1$ .

Simplify each term.

Apply the product rule to $\frac{2}{3}$ .

$y = 4 \cdot \frac{2^{0}}{3^{0}} + 1$

Anything raised to $0$ is $1$ .

$y = 4 \cdot \frac{1}{3^{0}} + 1$

Anything raised to $0$ is $1$ .

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

Cancel the common factor of $1$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 4 \cdot 1 + 1$

Multiply $4$ by $1$ .

$y = 4 + 1$

Add $4$ and $1$ .

$y = 5$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Simplify $4 \cdot (\frac{2}{3}) + 1$ .

Multiply $4 (\frac{2}{3})$ .

Combine $4$ and $\frac{2}{3}$ .

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

Multiply $4$ by $2$ .

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

Simplify the expression.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Add $8$ and $3$ .

$y = \frac{11}{3}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify each term.

Apply the product rule to $\frac{2}{3}$ .

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

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

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

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

$y = 4 \cdot \frac{4}{9} + 1$

Multiply $4 (\frac{4}{9})$ .

Combine $4$ and $\frac{4}{9}$ .

$y = \frac{4 \cdot 4}{9} + 1$

Multiply $4$ by $4$ .

$y = \frac{16}{9} + 1$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$y = \frac{16}{9} + \frac{9}{9}$

Combine the numerators over the common denominator.

$y = \frac{16 + 9}{9}$

Add $16$ and $9$ .

$y = \frac{25}{9}$

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

$\begin{array}{c} x & y \\ - 2 & 10 \\ - 1 & 7 \\ 0 & 5 \\ 1 & \frac{11}{3} \\ 2 & \frac{25}{9} \end{array}$

Graph Using a Table of Values f(x)=4*(2/3)^x+1

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