Graph g(x)=(x-3)^3

$g (x) = {(x - 3)}^{3}$

Step 1

Find the point at $x = 1$ .

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

$f (1) = {((1) - 3)}^{3}$

Simplify the result.

Subtract $3$ from $1$ .

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

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

$f (1) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 2

Find the point at $x = 2$ .

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

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

Simplify the result.

Subtract $3$ from $2$ .

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

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

$f (2) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Step 3

Find the point at $x = 3$ .

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

$f (3) = {((3) - 3)}^{3}$

Simplify the result.

Subtract $3$ from $3$ .

$f (3) = 0^{3}$

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

$f (3) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 4

Find the point at $x = 4$ .

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

$f (4) = {((4) - 3)}^{3}$

Simplify the result.

Subtract $3$ from $4$ .

$f (4) = 1^{3}$

One to any power is one.

$f (4) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 5

Find the point at $x = 5$ .

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

$f (5) = {((5) - 3)}^{3}$

Simplify the result.

Subtract $3$ from $5$ .

$f (5) = 2^{3}$

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

$f (5) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

Step 6

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

$\begin{array}{c} x & y \\ 1 & - 8 \\ 2 & - 1 \\ 3 & 0 \\ 4 & 1 \\ 5 & 8 \end{array}$

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

$\begin{array}{c} x & y \\ 1 & - 8 \\ 2 & - 1 \\ 3 & 0 \\ 4 & 1 \\ 5 & 8 \end{array}$

Step 8

Graph g(x)=(x-3)^3

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