Graph y=-(1/3x)^3+3

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

Find the point at $x = 0$ .

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

$f (0) = - \frac{{(0)}^{3}}{27} + 3$

Simplify the result.

Simplify each term.

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

$f (0) = - \frac{0}{27} + 3$

Divide $0$ by $27$ .

$f (0) = - 0 + 3$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 3$

Add $0$ and $3$ .

$f (0) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Find the point at $x = 3$ .

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

$f (3) = - \frac{{(3)}^{3}}{27} + 3$

Simplify the result.

Simplify each term.

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

$f (3) = - \frac{27}{27} + 3$

Cancel the common factor of $27$ .

Cancel the common factor.

$f (3) = - \frac{27}{27} + 3$

Rewrite the expression.

$f (3) = - 1 \cdot 1 + 3$

Multiply $- 1$ by $1$ .

$f (3) = - 1 + 3$

Add $- 1$ and $3$ .

$f (3) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

$f (- 2) = - \frac{- 8}{27} + 3$

Move the negative in front of the fraction.

$f (- 2) = \frac{8}{27} + 3$

Multiply $- - \frac{8}{27}$ .

Multiply $- 1$ by $- 1$ .

$f (- 2) = 1 (\frac{8}{27}) + 3$

Multiply $\frac{8}{27}$ by $1$ .

$f (- 2) = \frac{8}{27} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$f (- 2) = \frac{8}{27} + 3 \cdot \frac{27}{27}$

Combine $3$ and $\frac{27}{27}$ .

$f (- 2) = \frac{8}{27} + \frac{3 \cdot 27}{27}$

Combine the numerators over the common denominator.

$f (- 2) = \frac{8 + 3 \cdot 27}{27}$

Simplify the numerator.

Multiply $3$ by $27$ .

$f (- 2) = \frac{8 + 81}{27}$

Add $8$ and $81$ .

$f (- 2) = \frac{89}{27}$

The final answer is $\frac{89}{27}$ .

$\frac{89}{27}$

Convert $\frac{89}{27}$ to decimal.

$y = 3.\overline{296}$

Find the point at $x = - 1$ .

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

$f (- 1) = - \frac{{(- 1)}^{3}}{27} + 3$

Simplify the result.

Simplify each term.

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

$f (- 1) = - \frac{- 1}{27} + 3$

Move the negative in front of the fraction.

$f (- 1) = \frac{1}{27} + 3$

Multiply $- - \frac{1}{27}$ .

Multiply $- 1$ by $- 1$ .

$f (- 1) = 1 (\frac{1}{27}) + 3$

Multiply $\frac{1}{27}$ by $1$ .

$f (- 1) = \frac{1}{27} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$f (- 1) = \frac{1}{27} + 3 \cdot \frac{27}{27}$

Combine $3$ and $\frac{27}{27}$ .

$f (- 1) = \frac{1}{27} + \frac{3 \cdot 27}{27}$

Combine the numerators over the common denominator.

$f (- 1) = \frac{1 + 3 \cdot 27}{27}$

Simplify the numerator.

Multiply $3$ by $27$ .

$f (- 1) = \frac{1 + 81}{27}$

Add $1$ and $81$ .

$f (- 1) = \frac{82}{27}$

The final answer is $\frac{82}{27}$ .

$\frac{82}{27}$

Convert $\frac{82}{27}$ to decimal.

$y = 3.\overline{037}$

Find the point at $x = 1$ .

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

$f (1) = - \frac{{(1)}^{3}}{27} + 3$

Simplify the result.

One to any power is one.

$f (1) = - \frac{1}{27} + 3$

To write $3$ as a fraction with a common denominator, multiply by $\frac{27}{27}$ .

$f (1) = - \frac{1}{27} + 3 \cdot \frac{27}{27}$

Combine $3$ and $\frac{27}{27}$ .

$f (1) = - \frac{1}{27} + \frac{3 \cdot 27}{27}$

Combine the numerators over the common denominator.

$f (1) = \frac{- 1 + 3 \cdot 27}{27}$

Simplify the numerator.

Multiply $3$ by $27$ .

$f (1) = \frac{- 1 + 81}{27}$

Add $- 1$ and $81$ .

$f (1) = \frac{80}{27}$

The final answer is $\frac{80}{27}$ .

$\frac{80}{27}$

Convert $\frac{80}{27}$ to decimal.

$y = 2.\overline{962}$

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

$\begin{array}{c} x & y \\ - 2 & 3.296 \\ - 1 & 3.037 \\ 0 & 3 \\ 1 & 2.963 \\ 3 & 2 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 2 & 3.296 \\ - 1 & 3.037 \\ 0 & 3 \\ 1 & 2.963 \\ 3 & 2 \end{array}$

Graph y=-(1/3x)^3+3

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