Graph f(x)=(1-2x)^3

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

Step 1

Find the point at $x = - 1$ .

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

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

Simplify the result.

Multiply $- 2$ by $- 1$ .

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

Add $1$ and $2$ .

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

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

$f (- 1) = 27$

The final answer is $27$ .

$27$

Convert $27$ to decimal.

$y = 27$

Step 2

Find the point at $x = 0$ .

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

$f (0) = {(1 - 2 \cdot 0)}^{3}$

Simplify the result.

Multiply $- 2$ by $0$ .

$f (0) = {(1 + 0)}^{3}$

Add $1$ and $0$ .

$f (0) = 1^{3}$

One to any power is one.

$f (0) = 1$

The final answer is $1$ .

$1$

Convert $1$ to decimal.

$y = 1$

Step 3

Find the point at $x = 1$ .

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

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

Simplify the result.

Multiply $- 2$ by $1$ .

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

Subtract $2$ from $1$ .

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

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

$f (1) = - 1$

The final answer is $- 1$ .

$- 1$

Convert $- 1$ to decimal.

$y = - 1$

Step 4

Find the point at $x = 2$ .

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

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

Simplify the result.

Multiply $- 2$ by $2$ .

$f (2) = {(1 - 4)}^{3}$

Subtract $4$ from $1$ .

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

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

$f (2) = - 27$

The final answer is $- 27$ .

$- 27$

Convert $- 27$ to decimal.

$y = - 27$

Step 5

Find the point at $x = 3$ .

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

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

Simplify the result.

Multiply $- 2$ by $3$ .

$f (3) = {(1 - 6)}^{3}$

Subtract $6$ from $1$ .

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

Raise $- 5$ to the power of $3$ .

$f (3) = - 125$

The final answer is $- 125$ .

$- 125$

Convert $- 125$ to decimal.

$y = - 125$

Step 6

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

$\begin{array}{c} x & y \\ - 1 & 27 \\ 0 & 1 \\ 1 & - 1 \\ 2 & - 27 \\ 3 & - 125 \end{array}$

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

$\begin{array}{c} x & y \\ - 1 & 27 \\ 0 & 1 \\ 1 & - 1 \\ 2 & - 27 \\ 3 & - 125 \end{array}$

Step 8

Graph f(x)=(1-2x)^3

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