Graph y=-1/2(x-3)^3

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

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $3$ from $1$ .

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

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

$f (1) = - \frac{- 8}{2}$

Simplify the expression.

Divide $- 8$ by $2$ .

$f (1) = 4$

Multiply $- 1$ by $- 4$ .

$f (1) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Find the point at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

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

Simplify the result.

Simplify the numerator.

Subtract $3$ from $3$ .

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

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

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

Simplify the expression.

Divide $0$ by $2$ .

$f (3) = - 0$

Multiply $- 1$ by $0$ .

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = - \frac{{((5) - 3)}^{3}}{2}$

Simplify the result.

Simplify the numerator.

Subtract $3$ from $5$ .

$f (5) = - \frac{2^{3}}{2}$

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

$f (5) = - \frac{8}{2}$

Simplify the expression.

Divide $8$ by $2$ .

$f (5) = - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$f (5) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $3$ from $2$ .

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

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

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

Move the negative in front of the fraction.

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

The final answer is $\frac{1}{2}$ .

$\frac{1}{2}$

Convert $\frac{1}{2}$ to decimal.

$y = 0.5$

Find the point at $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

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

Simplify the result.

Simplify the numerator.

Subtract $3$ from $4$ .

$f (4) = - \frac{1^{3}}{2}$

One to any power is one.

$f (4) = - \frac{1}{2}$

The final answer is $- \frac{1}{2}$ .

$- \frac{1}{2}$

Convert $- \frac{1}{2}$ to decimal.

$y = - 0.5$

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

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0.5 \\ 3 & 0 \\ 4 & - 0.5 \\ 5 & - 4 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ 1 & 4 \\ 2 & 0.5 \\ 3 & 0 \\ 4 & - 0.5 \\ 5 & - 4 \end{array}$

Graph y=-1/2(x-3)^3

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