Graph y=(2x)^3+2

$y = {(2 x)}^{3} + 2$

Step 1

Find the point at $x = - 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $8$ by $- 8$ .

$f (- 2) = - 64 + 2$

Add $- 64$ and $2$ .

$f (- 2) = - 62$

The final answer is $- 62$ .

$- 62$

Convert $- 62$ to decimal.

$y = - 62$

Step 2

Find the point at $x = - 1$ .

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

$f (- 1) = 8 {(- 1)}^{3} + 2$

Simplify the result.

Simplify each term.

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

$f (- 1) = 8 \cdot - 1 + 2$

Multiply $8$ by $- 1$ .

$f (- 1) = - 8 + 2$

Add $- 8$ and $2$ .

$f (- 1) = - 6$

The final answer is $- 6$ .

$- 6$

Convert $- 6$ to decimal.

$y = - 6$

Step 3

Find the point at $x = 0$ .

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

$f (0) = 8 {(0)}^{3} + 2$

Simplify the result.

Simplify each term.

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

$f (0) = 8 \cdot 0 + 2$

Multiply $8$ by $0$ .

$f (0) = 0 + 2$

Add $0$ and $2$ .

$f (0) = 2$

The final answer is $2$ .

$2$

Convert $2$ to decimal.

$y = 2$

Step 4

Find the point at $x = 1$ .

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

$f (1) = 8 {(1)}^{3} + 2$

Simplify the result.

Simplify each term.

One to any power is one.

$f (1) = 8 \cdot 1 + 2$

Multiply $8$ by $1$ .

$f (1) = 8 + 2$

Add $8$ and $2$ .

$f (1) = 10$

The final answer is $10$ .

$10$

Convert $10$ to decimal.

$y = 10$

Step 5

Find the point at $x = 2$ .

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

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

Simplify the result.

Simplify each term.

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

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

Multiply $8$ by $8$ .

$f (2) = 64 + 2$

Add $64$ and $2$ .

$f (2) = 66$

The final answer is $66$ .

$66$

Convert $66$ to decimal.

$y = 66$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 62 \\ - 1 & - 6 \\ 0 & 2 \\ 1 & 10 \\ 2 & 66 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 62 \\ - 1 & - 6 \\ 0 & 2 \\ 1 & 10 \\ 2 & 66 \end{array}$

Step 8

Graph y=(2x)^3+2

Related Questions

Support LCMGCF.com by disabling your adblocker.