Graph y=3/2x^3

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

Step 1

Find the point at $x = - 2$ .

Replace the variable $x$ with $- 2$ in the expression.

$f (- 2) = \frac{3 {(- 2)}^{3}}{2}$

Simplify the result.

Cancel the common factor of ${(- 2)}^{3}$ and $2$ .

Rewrite $- 2$ as $- 1 (2)$ .

$f (- 2) = \frac{3 {(- 1 \cdot 2)}^{3}}{2}$

Apply the product rule to $- 1 (2)$ .

$f (- 2) = \frac{3 ({(- 1)}^{3} \cdot 2^{3})}{2}$

Raise $- 1$ to the power of $3$ .

$f (- 2) = \frac{3 (- 1 \cdot 2^{3})}{2}$

Factor $2$ out of $3 (- 1 \cdot 2^{3})$ .

$f (- 2) = \frac{2 (3 (- 1 \cdot 2^{2}))}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$f (- 2) = \frac{2 (3 (- 1 \cdot 2^{2}))}{2 (1)}$

Cancel the common factor.

$f (- 2) = \frac{2 (3 (- 1 \cdot 2^{2}))}{2 \cdot 1}$

Rewrite the expression.

$f (- 2) = \frac{3 (- 1 \cdot 2^{2})}{1}$

Divide $3 (- 1 \cdot 2^{2})$ by $1$ .

$f (- 2) = 3 (- 1 \cdot 2^{2})$

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

$f (- 2) = 3 (- 1 \cdot 4)$

Multiply $3 (- 1 \cdot 4)$ .

Multiply $- 1$ by $4$ .

$f (- 2) = 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$f (- 2) = - 12$

The final answer is $- 12$ .

$- 12$

Convert $- 12$ to decimal.

$y = - 12$

Step 2

Find the point at $x = 0$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = \frac{3 {(0)}^{3}}{2}$

Simplify the result.

Raising $0$ to any positive power yields $0$ .

$f (0) = \frac{3 \cdot 0}{2}$

Multiply $3$ by $0$ .

$f (0) = \frac{0}{2}$

Divide $0$ by $2$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 2$ .

Replace the variable $x$ with $2$ in the expression.

$f (2) = \frac{3 {(2)}^{3}}{2}$

Simplify the result.

Cancel the common factor of ${(2)}^{3}$ and $2$ .

Factor $2$ out of $3 {(2)}^{3}$ .

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

Cancel the common factors.

Factor $2$ out of $2$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Divide $3 \cdot 2^{2}$ by $1$ .

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

Simplify the expression.

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

$f (2) = 3 \cdot 4$

Multiply $3$ by $4$ .

$f (2) = 12$

The final answer is $12$ .

$12$

Convert $12$ to decimal.

$y = 12$

Step 4

Find the point at $x = - 1$ .

Replace the variable $x$ with $- 1$ in the expression.

$f (- 1) = \frac{3 {(- 1)}^{3}}{2}$

Simplify the result.

Raise $- 1$ to the power of $3$ .

$f (- 1) = \frac{3 \cdot - 1}{2}$

Multiply $3$ by $- 1$ .

$f (- 1) = \frac{- 3}{2}$

Move the negative in front of the fraction.

$f (- 1) = - \frac{3}{2}$

The final answer is $- \frac{3}{2}$ .

$- \frac{3}{2}$

Convert $- \frac{3}{2}$ to decimal.

$y = - 1.5$

Step 5

Find the point at $x = 1$ .

Replace the variable $x$ with $1$ in the expression.

$f (1) = \frac{3 {(1)}^{3}}{2}$

Simplify the result.

One to any power is one.

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

Multiply $3$ by $1$ .

$f (1) = \frac{3}{2}$

The final answer is $\frac{3}{2}$ .

$\frac{3}{2}$

Convert $\frac{3}{2}$ to decimal.

$y = 1.5$

Step 6

The cubic function can be graphed using the function behavior and the points.

$\begin{array}{c} x & y \\ - 2 & - 12 \\ - 1 & - 1.5 \\ 0 & 0 \\ 1 & 1.5 \\ 2 & 12 \end{array}$

Step 7

The cubic function can be graphed using the function behavior and the selected points.

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 2 & - 12 \\ - 1 & - 1.5 \\ 0 & 0 \\ 1 & 1.5 \\ 2 & 12 \end{array}$

Step 8

Graph y=3/2x^3

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