Graph h(x)=-3x^3+x^2-x+3

$h (x) = - 3 x^{3} + x^{2} - x + 3$

Find the point at $x = - 1$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $- 1$ .

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

Raise $- 1$ to the power of $2$ .

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

Multiply $- 1$ by $- 1$ .

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

Simplify by adding numbers.

Add $3$ and $1$ .

$f (- 1) = 4 + 1 + 3$

Add $4$ and $1$ .

$f (- 1) = 5 + 3$

Add $5$ and $3$ .

$f (- 1) = 8$

The final answer is $8$ .

$8$

Convert $8$ to decimal.

$y = 8$

Find the point at $x = 0$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $0$ .

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

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

$f (0) = 0 + 0 - (0) + 3$

Multiply $- 1$ by $0$ .

$f (0) = 0 + 0 + 0 + 3$

Simplify by adding numbers.

Add $0$ and $0$ .

$f (0) = 0 + 0 + 3$

Add $0$ and $0$ .

$f (0) = 0 + 3$

Add $0$ and $3$ .

$f (0) = 3$

The final answer is $3$ .

$3$

Convert $3$ to decimal.

$y = 3$

Find the point at $x = 1$ .

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

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

Simplify the result.

Simplify each term.

One to any power is one.

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

Multiply $- 3$ by $1$ .

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

One to any power is one.

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

Multiply $- 1$ by $1$ .

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

Simplify by adding and subtracting.

Add $- 3$ and $1$ .

$f (1) = - 2 - 1 + 3$

Subtract $1$ from $- 2$ .

$f (1) = - 3 + 3$

Add $- 3$ and $3$ .

$f (1) = 0$

The final answer is $0$ .

$0$

Convert $0$ to decimal.

$y = 0$

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $8$ .

$f (2) = - 24 + {(2)}^{2} - (2) + 3$

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

$f (2) = - 24 + 4 - (2) + 3$

Multiply $- 1$ by $2$ .

$f (2) = - 24 + 4 - 2 + 3$

Simplify by adding and subtracting.

Add $- 24$ and $4$ .

$f (2) = - 20 - 2 + 3$

Subtract $2$ from $- 20$ .

$f (2) = - 22 + 3$

Add $- 22$ and $3$ .

$f (2) = - 19$

The final answer is $- 19$ .

$- 19$

Convert $- 19$ to decimal.

$y = - 19$

Find the point at $x = 3$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $- 3$ by $27$ .

$f (3) = - 81 + {(3)}^{2} - (3) + 3$

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

$f (3) = - 81 + 9 - (3) + 3$

Multiply $- 1$ by $3$ .

$f (3) = - 81 + 9 - 3 + 3$

Simplify by adding and subtracting.

Add $- 81$ and $9$ .

$f (3) = - 72 - 3 + 3$

Subtract $3$ from $- 72$ .

$f (3) = - 75 + 3$

Add $- 75$ and $3$ .

$f (3) = - 72$

The final answer is $- 72$ .

$- 72$

Convert $- 72$ to decimal.

$y = - 72$

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

$\begin{array}{c} x & y \\ - 1 & 8 \\ 0 & 3 \\ 1 & 0 \\ 2 & - 19 \\ 3 & - 72 \end{array}$

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

Rises to the left and falls to the right

$\begin{array}{c} x & y \\ - 1 & 8 \\ 0 & 3 \\ 1 & 0 \\ 2 & - 19 \\ 3 & - 72 \end{array}$

Graph h(x)=-3x^3+x^2-x+3

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