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

$f (x) = 5^{x - 6} + 5$

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

$y = 5^{(- 2) - 6} + 5$

Simplify $5^{(- 2) - 6} + 5$ .

Simplify each term.

Subtract $6$ from $- 2$ .

$y = 5^{- 8} + 5$

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

$y = \frac{1}{5^{8}} + 5$

Raise $5$ to the power of $8$ .

$y = \frac{1}{390625} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{390625}{390625}$ .

$y = \frac{1}{390625} + 5 \cdot \frac{390625}{390625}$

Combine $5$ and $\frac{390625}{390625}$ .

$y = \frac{1}{390625} + \frac{5 \cdot 390625}{390625}$

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 390625}{390625}$

Simplify the numerator.

Multiply $5$ by $390625$ .

$y = \frac{1 + 1953125}{390625}$

Add $1$ and $1953125$ .

$y = \frac{1953126}{390625}$

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

$y = 5^{(- 1) - 6} + 5$

Simplify $5^{(- 1) - 6} + 5$ .

Simplify each term.

Subtract $6$ from $- 1$ .

$y = 5^{- 7} + 5$

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

$y = \frac{1}{5^{7}} + 5$

Raise $5$ to the power of $7$ .

$y = \frac{1}{78125} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{78125}{78125}$ .

$y = \frac{1}{78125} + 5 \cdot \frac{78125}{78125}$

Combine $5$ and $\frac{78125}{78125}$ .

$y = \frac{1}{78125} + \frac{5 \cdot 78125}{78125}$

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 78125}{78125}$

Simplify the numerator.

Multiply $5$ by $78125$ .

$y = \frac{1 + 390625}{78125}$

Add $1$ and $390625$ .

$y = \frac{390626}{78125}$

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

$y = 5^{(0) - 6} + 5$

Simplify $5^{(0) - 6} + 5$ .

Simplify each term.

Subtract $6$ from $0$ .

$y = 5^{- 6} + 5$

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

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

Raise $5$ to the power of $6$ .

$y = \frac{1}{15625} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{15625}{15625}$ .

$y = \frac{1}{15625} + 5 \cdot \frac{15625}{15625}$

Combine $5$ and $\frac{15625}{15625}$ .

$y = \frac{1}{15625} + \frac{5 \cdot 15625}{15625}$

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 15625}{15625}$

Simplify the numerator.

Multiply $5$ by $15625$ .

$y = \frac{1 + 78125}{15625}$

Add $1$ and $78125$ .

$y = \frac{78126}{15625}$

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

$y = 5^{(1) - 6} + 5$

Simplify $5^{(1) - 6} + 5$ .

Simplify each term.

Subtract $6$ from $1$ .

$y = 5^{- 5} + 5$

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

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

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

$y = \frac{1}{3125} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{3125}{3125}$ .

$y = \frac{1}{3125} + 5 \cdot \frac{3125}{3125}$

Combine $5$ and $\frac{3125}{3125}$ .

$y = \frac{1}{3125} + \frac{5 \cdot 3125}{3125}$

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 3125}{3125}$

Simplify the numerator.

Multiply $5$ by $3125$ .

$y = \frac{1 + 15625}{3125}$

Add $1$ and $15625$ .

$y = \frac{15626}{3125}$

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

$y = 5^{(2) - 6} + 5$

Simplify $5^{(2) - 6} + 5$ .

Simplify each term.

Subtract $6$ from $2$ .

$y = 5^{- 4} + 5$

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

$y = \frac{1}{5^{4}} + 5$

Raise $5$ to the power of $4$ .

$y = \frac{1}{625} + 5$

To write $5$ as a fraction with a common denominator, multiply by $\frac{625}{625}$ .

$y = \frac{1}{625} + 5 \cdot \frac{625}{625}$

Combine $5$ and $\frac{625}{625}$ .

$y = \frac{1}{625} + \frac{5 \cdot 625}{625}$

Combine the numerators over the common denominator.

$y = \frac{1 + 5 \cdot 625}{625}$

Simplify the numerator.

Multiply $5$ by $625$ .

$y = \frac{1 + 3125}{625}$

Add $1$ and $3125$ .

$y = \frac{3126}{625}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{1953126}{390625} \\ - 1 & \frac{390626}{78125} \\ 0 & \frac{78126}{15625} \\ 1 & \frac{15626}{3125} \\ 2 & \frac{3126}{625} \end{array}$

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

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