Graph Using a Table of Values f(x)=3*2^x

$f (x) = 3 \cdot 2^{x}$

Step 1

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

$y = 3 \cdot 2^{- 2}$

Step 2

Simplify $3 \cdot 2^{- 2}$ .

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

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

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

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

Combine $3$ and $\frac{1}{4}$ .

$y = \frac{3}{4}$

Step 3

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

$y = 3 \cdot 2^{- 1}$

Step 4

Simplify $3 \cdot 2^{- 1}$ .

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

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

Combine $3$ and $\frac{1}{2}$ .

$y = \frac{3}{2}$

Step 5

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

$y = 3 \cdot 2^{0}$

Step 6

Simplify $3 \cdot 2^{0}$ .

Anything raised to $0$ is $1$ .

$y = 3 \cdot 1$

Multiply $3$ by $1$ .

$y = 3$

Step 7

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

$y = 3 \cdot 2^{1}$

Step 8

Simplify $3 \cdot 2^{1}$ .

Evaluate the exponent.

$y = 3 \cdot 2$

Multiply $3$ by $2$ .

$y = 6$

Step 9

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

$y = 3 \cdot 2^{2}$

Step 10

Simplify $3 \cdot 2^{2}$ .

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

$y = 3 \cdot 4$

Multiply $3$ by $4$ .

$y = 12$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{3}{4} \\ - 1 & \frac{3}{2} \\ 0 & 3 \\ 1 & 6 \\ 2 & 12 \end{array}$

Step 12

Graph Using a Table of Values f(x)=3*2^x

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