Graph y=-3/4x^3

$y = - \frac{3}{4} x^{3}$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = - \frac{3 {(- 2)}^{3}}{4}$

Simplify the result.

Raise $- 2$ to the power of $3$ .

$f (- 2) = - \frac{3 \cdot - 8}{4}$

Multiply $3$ by $- 8$ .

$f (- 2) = - \frac{- 24}{4}$

Divide $- 24$ by $4$ .

$f (- 2) = 6$

The final answer is $6$ .

$6$

Convert $6$ to decimal.

$y = 6$

Step 2

Find the point at $x = 0$ .

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

$f (0) = - \frac{3 {(0)}^{3}}{4}$

Simplify the result.

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

$f (0) = - \frac{3 \cdot 0}{4}$

Multiply $3$ by $0$ .

$f (0) = - \frac{0}{4}$

Divide $0$ by $4$ .

$f (0) = - 0$

Multiply $- 1$ by $0$ .

$f (0) = 0$

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.

$f (2) = - \frac{3 {(2)}^{3}}{4}$

Simplify the result.

Raise $2$ to the power of $3$ .

$f (2) = - \frac{3 \cdot 8}{4}$

Multiply $3$ by $8$ .

$f (2) = - \frac{24}{4}$

Divide $24$ by $4$ .

$f (2) = - 1 \cdot 6$

Multiply $- 1$ by $6$ .

$f (2) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 4

Find the point at $x = - 1$ .

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

$f (- 1) = - \frac{3 {(- 1)}^{3}}{4}$

Simplify the result.

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

$f (- 1) = - \frac{3 \cdot - 1}{4}$

Multiply $3$ by $- 1$ .

$f (- 1) = - \frac{- 3}{4}$

Move the negative in front of the fraction.

$f (- 1) = \frac{3}{4}$

The final answer is $\frac{3}{4}$ .

$\frac{3}{4}$

Convert $\frac{3}{4}$ to decimal.

$y = 0.75$

Step 5

Find the point at $x = 1$ .

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

$f (1) = - \frac{3 {(1)}^{3}}{4}$

Simplify the result.

One to any power is one.

$f (1) = - \frac{3 \cdot 1}{4}$

Multiply $3$ by $1$ .

$f (1) = - \frac{3}{4}$

The final answer is $- \frac{3}{4}$ .

$- \frac{3}{4}$

Convert $- \frac{3}{4}$ to decimal.

$y = - 0.75$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & 0.75 \\ 0 & 0 \\ 1 & - 0.75 \\ 2 & - 6 \end{array}$

Step 7

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & 0.75 \\ 0 & 0 \\ 1 & - 0.75 \\ 2 & - 6 \end{array}$

Step 8

Graph y=-3/4x^3

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