Algebra Examples

$V = \frac{4}{3} π r^{3}$

Step 1

Find the point at $x = 0$ .

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Step 1.1

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

$f (0) = \frac{4 π {(0)}^{3}}{3}$

Step 1.2

Simplify the result.

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Step 1.2.1

Simplify the numerator.

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Step 1.2.1.1

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

$f (0) = \frac{4 π \cdot 0}{3}$

Step 1.2.1.2

Combine exponents.

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Step 1.2.1.2.1

Multiply $0$ by $4$ .

$f (0) = \frac{0 π}{3}$

Step 1.2.1.2.2

Multiply $0$ by $π$ .

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

Step 1.2.2

Divide $0$ by $3$ .

$f (0) = 0$

Step 1.2.3

The final answer is $0$ .

$0$

Step 1.3

Convert $0$ to decimal.

$y = 0$

Step 2

Find the point at $x = - 2$ .

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Step 2.1

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

$f (- 2) = \frac{4 π {(- 2)}^{3}}{3}$

Step 2.2

Simplify the result.

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

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

$f (- 2) = \frac{4 π \cdot - 8}{3}$

Step 2.2.1.2

Multiply $- 8$ by $4$ .

$f (- 2) = \frac{- 32 π}{3}$

Step 2.2.2

Move the negative in front of the fraction.

$f (- 2) = - \frac{32 π}{3}$

Step 2.2.3

The final answer is $- \frac{32 π}{3}$ .

$- \frac{32 π}{3}$

Step 2.3

Convert $- \frac{32 π}{3}$ to decimal.

$y = - 33.51032163$

Step 3

Find the point at $x = - 1$ .

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Step 3.1

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

$f (- 1) = \frac{4 π {(- 1)}^{3}}{3}$

Step 3.2

Simplify the result.

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Step 3.2.1

Simplify the numerator.

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Step 3.2.1.1

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

$f (- 1) = \frac{4 π \cdot - 1}{3}$

Step 3.2.1.2

Multiply $- 1$ by $4$ .

$f (- 1) = \frac{- 4 π}{3}$

Step 3.2.2

Move the negative in front of the fraction.

$f (- 1) = - \frac{4 π}{3}$

Step 3.2.3

The final answer is $- \frac{4 π}{3}$ .

$- \frac{4 π}{3}$

Step 3.3

Convert $- \frac{4 π}{3}$ to decimal.

$y = - 4.1887902$

Step 4

Find the point at $x = 1$ .

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Step 4.1

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

$f (1) = \frac{4 π {(1)}^{3}}{3}$

Step 4.2

Simplify the result.

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

One to any power is one.

$f (1) = \frac{4 π \cdot 1}{3}$

Step 4.2.1.2

Multiply $4$ by $1$ .

$f (1) = \frac{4 π}{3}$

Step 4.2.2

The final answer is $\frac{4 π}{3}$ .

$\frac{4 π}{3}$

Step 4.3

Convert $\frac{4 π}{3}$ to decimal.

$y = 4.1887902$

Step 5

Find the point at $x = 2$ .

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Step 5.1

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

$f (2) = \frac{4 π {(2)}^{3}}{3}$

Step 5.2

Simplify the result.

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Step 5.2.1

Simplify the numerator.

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Step 5.2.1.1

Rewrite $4$ as $2^{2}$ .

$f (2) = \frac{2^{3} \cdot (2^{2} π)}{3}$

Step 5.2.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$f (2) = \frac{2^{3 + 2} π}{3}$

Step 5.2.1.3

Add $3$ and $2$ .

$f (2) = \frac{2^{5} π}{3}$

Step 5.2.2

Raise $2$ to the power of $5$ .

$f (2) = \frac{32 π}{3}$

Step 5.2.3

The final answer is $\frac{32 π}{3}$ .

$\frac{32 π}{3}$

Step 5.3

Convert $\frac{32 π}{3}$ to decimal.

$y = 33.51032163$

Step 6

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

$\begin{array}{c} x & y \\ - 2 & - 33.51 \\ - 1 & - 4.189 \\ 0 & 0 \\ 1 & 4.189 \\ 2 & 33.51 \end{array}$

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

$\begin{array}{c} x & y \\ - 2 & - 33.51 \\ - 1 & - 4.189 \\ 0 & 0 \\ 1 & 4.189 \\ 2 & 33.51 \end{array}$

Step 8