Graph f(x)=x^3-x^2-2

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

Step 1

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{2}$ .

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

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

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

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

Add $1$ and $2$ .

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

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

$f (- 1) = - 1 - 1 - 2$

Simplify by subtracting numbers.

Subtract $1$ from $- 1$ .

$f (- 1) = - 2 - 2$

Subtract $2$ from $- 2$ .

$f (- 1) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 2

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

$f (0) = 0 - {(0)}^{2} - 2$

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

$f (0) = 0 - 0 - 2$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 - 2$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 - 2$

Subtract $2$ from $0$ .

$f (0) = - 2$

The final answer is $- 2$ .

$- 2$

Convert $- 2$ to decimal.

$y = - 2$

Step 3

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (2) = 8 - {(2)}^{2} - 2$

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

$f (2) = 8 - 1 \cdot 4 - 2$

Multiply $- 1$ by $4$ .

$f (2) = 8 - 4 - 2$

Simplify by subtracting numbers.

Subtract $4$ from $8$ .

$f (2) = 4 - 2$

Subtract $2$ from $4$ .

$f (2) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

$f (3) = 27 - {(3)}^{2} - 2$

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

$f (3) = 27 - 1 \cdot 9 - 2$

Multiply $- 1$ by $9$ .

$f (3) = 27 - 9 - 2$

Simplify by subtracting numbers.

Subtract $9$ from $27$ .

$f (3) = 18 - 2$

Subtract $2$ from $18$ .

$f (3) = 16$

The final answer is $16$ .

$16$

Convert $16$ to decimal.

$y = 16$

Step 5

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

$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & - 2 \\ 1 & - 2 \\ 2 & 2 \\ 3 & 16 \end{array}$

Step 6

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

Falls to the left and rises to the right

$\begin{array}{c} x & y \\ - 1 & - 4 \\ 0 & - 2 \\ 1 & - 2 \\ 2 & 2 \\ 3 & 16 \end{array}$

Step 7

Graph f(x)=x^3-x^2-2

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