Graph f(x)=x^3-3/400x

$f (x) = x^{3} - \frac{3}{400} x$

Step 1

Find the point at $x = 0$ .

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

$f (0) = {(0)}^{3} - \frac{3 (0)}{400}$

Simplify the result.

Simplify each term.

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

$f (0) = 0 - \frac{3 (0)}{400}$

Cancel the common factor of $0$ and $400$ .

Factor $400$ out of $3 (0)$ .

$f (0) = 0 - \frac{400 (3 \cdot (0))}{400}$

Cancel the common factors.

Factor $400$ out of $400$ .

$f (0) = 0 - \frac{400 (3 \cdot (0))}{400 (1)}$

Cancel the common factor.

$f (0) = 0 - \frac{400 (3 \cdot (0))}{400 \cdot 1}$

Rewrite the expression.

$f (0) = 0 - \frac{3 \cdot (0)}{1}$

Divide $3 \cdot (0)$ by $1$ .

$f (0) = 0 - (3 \cdot (0))$

Multiply $- (3 \cdot (0))$ .

Multiply $3$ by $0$ .

$f (0) = 0 - 0$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0$

Add $0$ and $0$ .

$f (0) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = - 2$ .

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

$f (- 2) = {(- 2)}^{3} - \frac{3 (- 2)}{400}$

Simplify the result.

Simplify each term.

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

$f (- 2) = - 8 - \frac{3 (- 2)}{400}$

Cancel the common factor of $- 2$ and $400$ .

Factor $2$ out of $3 (- 2)$ .

$f (- 2) = - 8 - \frac{2 (3 \cdot (- 1))}{400}$

Cancel the common factors.

Factor $2$ out of $400$ .

$f (- 2) = - 8 - \frac{2 (3 \cdot (- 1))}{2 (200)}$

Cancel the common factor.

$f (- 2) = - 8 - \frac{2 (3 \cdot (- 1))}{2 \cdot 200}$

Rewrite the expression.

$f (- 2) = - 8 - \frac{3 \cdot (- 1)}{200}$

Multiply $3$ by $- 1$ .

$f (- 2) = - 8 - \frac{- 3}{200}$

Move the negative in front of the fraction.

$f (- 2) = - 8 + \frac{3}{200}$

Multiply $- - \frac{3}{200}$ .

Multiply $- 1$ by $- 1$ .

$f (- 2) = - 8 + 1 (\frac{3}{200})$

Multiply $\frac{3}{200}$ by $1$ .

$f (- 2) = - 8 + \frac{3}{200}$

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{200}{200}$ .

$f (- 2) = - 8 \cdot \frac{200}{200} + \frac{3}{200}$

Combine $- 8$ and $\frac{200}{200}$ .

$f (- 2) = \frac{- 8 \cdot 200}{200} + \frac{3}{200}$

Combine the numerators over the common denominator.

$f (- 2) = \frac{- 8 \cdot 200 + 3}{200}$

Simplify the numerator.

Multiply $- 8$ by $200$ .

$f (- 2) = \frac{- 1600 + 3}{200}$

Add $- 1600$ and $3$ .

$f (- 2) = \frac{- 1597}{200}$

Move the negative in front of the fraction.

$f (- 2) = - \frac{1597}{200}$

The final answer is $- \frac{1597}{200}$ .

$- \frac{1597}{200}$

Convert $- \frac{1597}{200}$ to decimal.

$y = - 7.985$

Step 3

Find the point at $x = - 1$ .

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

$f (- 1) = {(- 1)}^{3} - \frac{3 (- 1)}{400}$

Simplify the result.

Simplify each term.

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

$f (- 1) = - 1 - \frac{3 (- 1)}{400}$

Multiply $3$ by $- 1$ .

$f (- 1) = - 1 - \frac{- 3}{400}$

Move the negative in front of the fraction.

$f (- 1) = - 1 + \frac{3}{400}$

Multiply $- - \frac{3}{400}$ .

Multiply $- 1$ by $- 1$ .

$f (- 1) = - 1 + 1 (\frac{3}{400})$

Multiply $\frac{3}{400}$ by $1$ .

$f (- 1) = - 1 + \frac{3}{400}$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{400}{400}$ .

$f (- 1) = - 1 \cdot \frac{400}{400} + \frac{3}{400}$

Combine $- 1$ and $\frac{400}{400}$ .

$f (- 1) = \frac{- 1 \cdot 400}{400} + \frac{3}{400}$

Combine the numerators over the common denominator.

$f (- 1) = \frac{- 1 \cdot 400 + 3}{400}$

Simplify the numerator.

Multiply $- 1$ by $400$ .

$f (- 1) = \frac{- 400 + 3}{400}$

Add $- 400$ and $3$ .

$f (- 1) = \frac{- 397}{400}$

Move the negative in front of the fraction.

$f (- 1) = - \frac{397}{400}$

The final answer is $- \frac{397}{400}$ .

$- \frac{397}{400}$

Convert $- \frac{397}{400}$ to decimal.

$y = - 0.9925$

Step 4

Find the point at $x = 1$ .

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

$f (1) = {(1)}^{3} - \frac{3 (1)}{400}$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 1 - \frac{3 (1)}{400}$

Multiply $3$ by $1$ .

$f (1) = 1 - \frac{3}{400}$

Simplify the expression.

Write $1$ as a fraction with a common denominator.

$f (1) = \frac{400}{400} - \frac{3}{400}$

Combine the numerators over the common denominator.

$f (1) = \frac{400 - 3}{400}$

Subtract $3$ from $400$ .

$f (1) = \frac{397}{400}$

The final answer is $\frac{397}{400}$ .

$\frac{397}{400}$

Convert $\frac{397}{400}$ to decimal.

$y = 0.9925$

Step 5

Find the point at $x = 2$ .

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

$f (2) = {(2)}^{3} - \frac{3 (2)}{400}$

Simplify the result.

Simplify each term.

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

$f (2) = 8 - \frac{3 (2)}{400}$

Cancel the common factor of $2$ and $400$ .

Factor $2$ out of $3 (2)$ .

$f (2) = 8 - \frac{2 \cdot 3}{400}$

Cancel the common factors.

Factor $2$ out of $400$ .

$f (2) = 8 - \frac{2 \cdot 3}{2 \cdot 200}$

Cancel the common factor.

$f (2) = 8 - \frac{2 \cdot 3}{2 \cdot 200}$

Rewrite the expression.

$f (2) = 8 - \frac{3}{200}$

To write $8$ as a fraction with a common denominator, multiply by $\frac{200}{200}$ .

$f (2) = 8 \cdot \frac{200}{200} - \frac{3}{200}$

Combine $8$ and $\frac{200}{200}$ .

$f (2) = \frac{8 \cdot 200}{200} - \frac{3}{200}$

Combine the numerators over the common denominator.

$f (2) = \frac{8 \cdot 200 - 3}{200}$

Simplify the numerator.

Multiply $8$ by $200$ .

$f (2) = \frac{1600 - 3}{200}$

Subtract $3$ from $1600$ .

$f (2) = \frac{1597}{200}$

The final answer is $\frac{1597}{200}$ .

$\frac{1597}{200}$

Convert $\frac{1597}{200}$ to decimal.

$y = 7.985$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 7.985 \\ - 1 & - 0.992 \\ 0 & 0 \\ 1 & 0.992 \\ 2 & 7.985 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 7.985 \\ - 1 & - 0.992 \\ 0 & 0 \\ 1 & 0.992 \\ 2 & 7.985 \end{array}$

Step 8

Graph f(x)=x^3-3/400x

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