Graph y=(-x)^3+1

$y = {(- x)}^{3} + 1$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (- 2) = 8 + 1$

Multiply $- 1$ by $- 8$ .

$f (- 2) = 8 + 1$

Add $8$ and $1$ .

$f (- 2) = 9$

The final answer is $9$ .

$9$

Convert $9$ to decimal.

$y = 9$

Step 2

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

Multiply $- 1$ by ${(- 1)}^{3}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{3}$ .

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

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $1$ and $3$ .

$f (- 1) = {(- 1)}^{4} + 1$

Raise $- 1$ to the power of $4$ .

$f (- 1) = 1 + 1$

Add $1$ and $1$ .

$f (- 1) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 3

Find the point at $x = 0$ .

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

$f (0) = - {(0)}^{3} + 1$

Simplify the result.

Simplify each term.

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

$f (0) = - 0 + 1$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 1$

Add $0$ and $1$ .

$f (0) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 4

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = - 1 \cdot 1 + 1$

Multiply $- 1$ by $1$ .

$f (1) = - 1 + 1$

Add $- 1$ and $1$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (2) = - 1 \cdot 8 + 1$

Multiply $- 1$ by $8$ .

$f (2) = - 8 + 1$

Add $- 8$ and $1$ .

$f (2) = - 7$

The final answer is $- 7$ .

$- 7$

Convert $- 7$ to decimal.

$y = - 7$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 9 \\ - 1 & 2 \\ 0 & 1 \\ 1 & 0 \\ 2 & - 7 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 9 \\ - 1 & 2 \\ 0 & 1 \\ 1 & 0 \\ 2 & - 7 \end{array}$

Step 8

Graph y=(-x)^3+1

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