Graph Using a Table of Values f(x)=-1/3*6^x+5

$f (x) = - \frac{1}{3} \cdot 6^{x} + 5$

Step 1

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

$y = - \frac{1}{3} \cdot 6^{- 2} + 5$

Step 2

Simplify $- \frac{1}{3} \cdot 6^{- 2} + 5$ .

Simplify each term.

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

$y = - \frac{1}{3} \cdot \frac{1}{6^{2}} + 5$

Raise $6$ to the power of $2$ .

$y = - \frac{1}{3} \cdot \frac{1}{36} + 5$

Multiply $- \frac{1}{3} \cdot \frac{1}{36}$ .

Multiply $\frac{1}{36}$ by $\frac{1}{3}$ .

$y = - \frac{1}{36 \cdot 3} + 5$

Multiply $36$ by $3$ .

$y = - \frac{1}{108} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{108}{108}$ .

$y = - \frac{1}{108} + 5 \cdot \frac{108}{108}$

Combine $5$ and $\frac{108}{108}$ .

$y = - \frac{1}{108} + \frac{5 \cdot 108}{108}$

Combine the numerators over the common denominator.

$y = \frac{- 1 + 5 \cdot 108}{108}$

Simplify the numerator.

Multiply $5$ by $108$ .

$y = \frac{- 1 + 540}{108}$

Add $- 1$ and $540$ .

$y = \frac{539}{108}$

Step 3

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

$y = - \frac{1}{3} \cdot 6^{- 1} + 5$

Step 4

Simplify $- \frac{1}{3} \cdot 6^{- 1} + 5$ .

Simplify each term.

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

$y = - \frac{1}{3} \cdot \frac{1}{6} + 5$

Multiply $- \frac{1}{3} \cdot \frac{1}{6}$ .

Multiply $\frac{1}{6}$ by $\frac{1}{3}$ .

$y = - \frac{1}{6 \cdot 3} + 5$

Multiply $6$ by $3$ .

$y = - \frac{1}{18} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{18}{18}$ .

$y = - \frac{1}{18} + 5 \cdot \frac{18}{18}$

Combine $5$ and $\frac{18}{18}$ .

$y = - \frac{1}{18} + \frac{5 \cdot 18}{18}$

Combine the numerators over the common denominator.

$y = \frac{- 1 + 5 \cdot 18}{18}$

Simplify the numerator.

Multiply $5$ by $18$ .

$y = \frac{- 1 + 90}{18}$

Add $- 1$ and $90$ .

$y = \frac{89}{18}$

Step 5

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

$y = - \frac{1}{3} \cdot 6^{0} + 5$

Step 6

Simplify $- \frac{1}{3} \cdot 6^{0} + 5$ .

Simplify each term.

Anything raised to $0$ is $1$ .

$y = - \frac{1}{3} \cdot 1 + 5$

Multiply $- 1$ by $1$ .

$y = - \frac{1}{3} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{1}{3} + 5 \cdot \frac{3}{3}$

Combine $5$ and $\frac{3}{3}$ .

$y = - \frac{1}{3} + \frac{5 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 1 + 5 \cdot 3}{3}$

Simplify the numerator.

Multiply $5$ by $3$ .

$y = \frac{- 1 + 15}{3}$

Add $- 1$ and $15$ .

$y = \frac{14}{3}$

Step 7

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

$y = - \frac{1}{3} \cdot 6^{1} + 5$

Step 8

Simplify $- \frac{1}{3} \cdot 6^{1} + 5$ .

Simplify each term.

Evaluate the exponent.

$y = - \frac{1}{3} \cdot 6 + 5$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$y = \frac{- 1}{3} \cdot 6 + 5$

Factor $3$ out of $6$ .

$y = \frac{- 1}{3} \cdot (3 (2)) + 5$

Cancel the common factor.

$y = \frac{- 1}{3} \cdot (3 \cdot 2) + 5$

Rewrite the expression.

$y = - 1 \cdot 2 + 5$

Multiply $- 1$ by $2$ .

$y = - 2 + 5$

Add $- 2$ and $5$ .

$y = 3$

Step 9

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

$y = - \frac{1}{3} \cdot 6^{2} + 5$

Step 10

Simplify $- \frac{1}{3} \cdot 6^{2} + 5$ .

Simplify each term.

Raise $6$ to the power of $2$ .

$y = - \frac{1}{3} \cdot 36 + 5$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$y = \frac{- 1}{3} \cdot 36 + 5$

Factor $3$ out of $36$ .

$y = \frac{- 1}{3} \cdot (3 (12)) + 5$

Cancel the common factor.

$y = \frac{- 1}{3} \cdot (3 \cdot 12) + 5$

Rewrite the expression.

$y = - 1 \cdot 12 + 5$

Multiply $- 1$ by $12$ .

$y = - 12 + 5$

Add $- 12$ and $5$ .

$y = - 7$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{539}{108} \\ - 1 & \frac{89}{18} \\ 0 & \frac{14}{3} \\ 1 & 3 \\ 2 & - 7 \end{array}$

Step 12

Graph Using a Table of Values f(x)=-1/3*6^x+5

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