Graph f(x)=-5x^3+x-8

$f (x) = - 5 x^{3} + x - 8$

Step 1

Find the point at $x = - 2$ .

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

$f (- 2) = - 5 {(- 2)}^{3} - 2 - 8$

Simplify the result.

Remove parentheses.

$f (- 2) = - 5 {(- 2)}^{3} - 2 - 8$

Simplify each term.

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

$f (- 2) = - 5 \cdot - 8 - 2 - 8$

Multiply $- 5$ by $- 8$ .

$f (- 2) = 40 - 2 - 8$

Simplify by subtracting numbers.

Subtract $2$ from $40$ .

$f (- 2) = 38 - 8$

Subtract $8$ from $38$ .

$f (- 2) = 30$

The final answer is $30$ .

$30$

Convert $30$ to decimal.

$y = 30$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = - 5 {(- 1)}^{3} - 1 - 8$

Simplify the result.

Remove parentheses.

$f (- 1) = - 5 {(- 1)}^{3} - 1 - 8$

Simplify each term.

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

$f (- 1) = - 5 \cdot - 1 - 1 - 8$

Multiply $- 5$ by $- 1$ .

$f (- 1) = 5 - 1 - 8$

Simplify by subtracting numbers.

Subtract $1$ from $5$ .

$f (- 1) = 4 - 8$

Subtract $8$ from $4$ .

$f (- 1) = - 4$

The final answer is $- 4$ .

$- 4$

Convert $- 4$ to decimal.

$y = - 4$

Step 3

Find the point at $x = 0$ .

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

$f (0) = - 5 {(0)}^{3} + 0 - 8$

Simplify the result.

Remove parentheses.

$f (0) = - 5 {(0)}^{3} + 0 - 8$

Simplify each term.

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

$f (0) = - 5 \cdot 0 + 0 - 8$

Multiply $- 5$ by $0$ .

$f (0) = 0 + 0 - 8$

Simplify by adding and subtracting.

Add $0$ and $0$ .

$f (0) = 0 - 8$

Subtract $8$ from $0$ .

$f (0) = - 8$

The final answer is $- 8$ .

$- 8$

Convert $- 8$ to decimal.

$y = - 8$

Step 4

Find the point at $x = 1$ .

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

$f (1) = - 5 {(1)}^{3} + 1 - 8$

Simplify the result.

Remove parentheses.

$f (1) = - 5 {(1)}^{3} + 1 - 8$

Simplify each term.

One to any power is one.

$f (1) = - 5 \cdot 1 + 1 - 8$

Multiply $- 5$ by $1$ .

$f (1) = - 5 + 1 - 8$

Simplify by adding and subtracting.

Add $- 5$ and $1$ .

$f (1) = - 4 - 8$

Subtract $8$ from $- 4$ .

$f (1) = - 12$

The final answer is $- 12$ .

$- 12$

Convert $- 12$ to decimal.

$y = - 12$

Step 5

Find the point at $x = 2$ .

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

$f (2) = - 5 {(2)}^{3} + 2 - 8$

Simplify the result.

Remove parentheses.

$f (2) = - 5 {(2)}^{3} + 2 - 8$

Simplify each term.

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

$f (2) = - 5 \cdot 8 + 2 - 8$

Multiply $- 5$ by $8$ .

$f (2) = - 40 + 2 - 8$

Simplify by adding and subtracting.

Add $- 40$ and $2$ .

$f (2) = - 38 - 8$

Subtract $8$ from $- 38$ .

$f (2) = - 46$

The final answer is $- 46$ .

$- 46$

Convert $- 46$ to decimal.

$y = - 46$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & 30 \\ - 1 & - 4 \\ 0 & - 8 \\ 1 & - 12 \\ 2 & - 46 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & 30 \\ - 1 & - 4 \\ 0 & - 8 \\ 1 & - 12 \\ 2 & - 46 \end{array}$

Step 8

Graph f(x)=-5x^3+x-8

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