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

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

Step 1

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $2$ from $0$ .

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

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

$f (0) = \frac{- 8}{2}$

Divide $- 8$ by $2$ .

$f (0) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 2

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $2$ from $2$ .

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

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

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

Divide $0$ by $2$ .

$f (2) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 3

Find the point at $x = 4$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $2$ from $4$ .

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

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

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

Divide $8$ by $2$ .

$f (4) = 4$

The final answer is $4$ .

$4$

Convert $4$ to decimal.

$y = 4$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $2$ from $1$ .

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

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

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

Move the negative in front of the fraction.

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

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

$- \frac{1}{2}$

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

$y = - 0.5$

Step 5

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify the numerator.

Subtract $2$ from $3$ .

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

One to any power is one.

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

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

$\frac{1}{2}$

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

$y = 0.5$

Step 6

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

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

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

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

Step 8

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

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