Graph Using a Table of Values f(x)=(1/5)^(x+4)+3

$f (x) = {(\frac{1}{5})}^{x + 4} + 3$

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

$y = {(\frac{1}{5})}^{(- 2) + 4} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{5})}^{- 2 + 4} + 3$

Remove parentheses.

$y = {(\frac{1}{5})}^{(- 2) + 4} + 3$

Simplify ${(\frac{1}{5})}^{(- 2) + 4} + 3$ .

Simplify each term.

Add $- 2$ and $4$ .

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

Apply the product rule to $\frac{1}{5}$ .

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

One to any power is one.

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

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

$y = \frac{1}{25} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

$y = \frac{1}{25} + 3 \cdot \frac{25}{25}$

Combine $3$ and $\frac{25}{25}$ .

$y = \frac{1}{25} + \frac{3 \cdot 25}{25}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 25}{25}$

Simplify the numerator.

Multiply $3$ by $25$ .

$y = \frac{1 + 75}{25}$

Add $1$ and $75$ .

$y = \frac{76}{25}$

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

$y = {(\frac{1}{5})}^{(- 1) + 4} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{5})}^{- 1 + 4} + 3$

Remove parentheses.

$y = {(\frac{1}{5})}^{(- 1) + 4} + 3$

Simplify ${(\frac{1}{5})}^{(- 1) + 4} + 3$ .

Simplify each term.

Add $- 1$ and $4$ .

$y = {(\frac{1}{5})}^{3} + 3$

Apply the product rule to $\frac{1}{5}$ .

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

One to any power is one.

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

Raise $5$ to the power of $3$ .

$y = \frac{1}{125} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{125}{125}$ .

$y = \frac{1}{125} + 3 \cdot \frac{125}{125}$

Combine $3$ and $\frac{125}{125}$ .

$y = \frac{1}{125} + \frac{3 \cdot 125}{125}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 125}{125}$

Simplify the numerator.

Multiply $3$ by $125$ .

$y = \frac{1 + 375}{125}$

Add $1$ and $375$ .

$y = \frac{376}{125}$

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

$y = {(\frac{1}{5})}^{(0) + 4} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{5})}^{0 + 4} + 3$

Remove parentheses.

$y = {(\frac{1}{5})}^{(0) + 4} + 3$

Simplify ${(\frac{1}{5})}^{(0) + 4} + 3$ .

Simplify each term.

Add $0$ and $4$ .

$y = {(\frac{1}{5})}^{4} + 3$

Apply the product rule to $\frac{1}{5}$ .

$y = \frac{1^{4}}{5^{4}} + 3$

One to any power is one.

$y = \frac{1}{5^{4}} + 3$

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

$y = \frac{1}{625} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{625}{625}$ .

$y = \frac{1}{625} + 3 \cdot \frac{625}{625}$

Combine $3$ and $\frac{625}{625}$ .

$y = \frac{1}{625} + \frac{3 \cdot 625}{625}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 625}{625}$

Simplify the numerator.

Multiply $3$ by $625$ .

$y = \frac{1 + 1875}{625}$

Add $1$ and $1875$ .

$y = \frac{1876}{625}$

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

$y = {(\frac{1}{5})}^{(1) + 4} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{5})}^{1 + 4} + 3$

Remove parentheses.

$y = {(\frac{1}{5})}^{(1) + 4} + 3$

Simplify ${(\frac{1}{5})}^{(1) + 4} + 3$ .

Simplify each term.

Add $1$ and $4$ .

$y = {(\frac{1}{5})}^{5} + 3$

Apply the product rule to $\frac{1}{5}$ .

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

One to any power is one.

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

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

$y = \frac{1}{3125} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{3125}{3125}$ .

$y = \frac{1}{3125} + 3 \cdot \frac{3125}{3125}$

Combine $3$ and $\frac{3125}{3125}$ .

$y = \frac{1}{3125} + \frac{3 \cdot 3125}{3125}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 3125}{3125}$

Simplify the numerator.

Multiply $3$ by $3125$ .

$y = \frac{1 + 9375}{3125}$

Add $1$ and $9375$ .

$y = \frac{9376}{3125}$

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

$y = {(\frac{1}{5})}^{(2) + 4} + 3$

Solve the equation for $y$ .

Remove parentheses.

$y = {(\frac{1}{5})}^{2 + 4} + 3$

Remove parentheses.

$y = {(\frac{1}{5})}^{(2) + 4} + 3$

Simplify ${(\frac{1}{5})}^{(2) + 4} + 3$ .

Simplify each term.

Add $2$ and $4$ .

$y = {(\frac{1}{5})}^{6} + 3$

Apply the product rule to $\frac{1}{5}$ .

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

One to any power is one.

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

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

$y = \frac{1}{15625} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{15625}{15625}$ .

$y = \frac{1}{15625} + 3 \cdot \frac{15625}{15625}$

Combine $3$ and $\frac{15625}{15625}$ .

$y = \frac{1}{15625} + \frac{3 \cdot 15625}{15625}$

Combine the numerators over the common denominator.

$y = \frac{1 + 3 \cdot 15625}{15625}$

Simplify the numerator.

Multiply $3$ by $15625$ .

$y = \frac{1 + 46875}{15625}$

Add $1$ and $46875$ .

$y = \frac{46876}{15625}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{76}{25} \\ - 1 & \frac{376}{125} \\ 0 & \frac{1876}{625} \\ 1 & \frac{9376}{3125} \\ 2 & \frac{46876}{15625} \end{array}$

Graph Using a Table of Values f(x)=(1/5)^(x+4)+3

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