Algebra Examples

$g (x) = \frac{1}{4} {(x - 3)}^{3} + 4$

Step 1

Find the point at $x = 1$ .

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Step 1.1

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

$f (1) = \frac{{((1) - 3)}^{3} + 16}{4}$

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

Subtract $3$ from $1$ .

$f (1) = \frac{{(- 2)}^{3} + 16}{4}$

Step 1.2.1.2

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

$f (1) = \frac{- 8 + 16}{4}$

Step 1.2.1.3

Add $- 8$ and $16$ .

$f (1) = \frac{8}{4}$

Step 1.2.2

Divide $8$ by $4$ .

$f (1) = 2$

Step 1.2.3

The final answer is $2$ .

$2$

Step 1.3

Convert $2$ to decimal.

$y = 2$

Step 2

Find the point at $x = 3$ .

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Step 2.1

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

$f (3) = \frac{{((3) - 3)}^{3} + 16}{4}$

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

Subtract $3$ from $3$ .

$f (3) = \frac{0^{3} + 16}{4}$

Step 2.2.1.2

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

$f (3) = \frac{0 + 16}{4}$

Step 2.2.1.3

Add $0$ and $16$ .

$f (3) = \frac{16}{4}$

Step 2.2.2

Divide $16$ by $4$ .

$f (3) = 4$

Step 2.2.3

The final answer is $4$ .

$4$

Step 2.3

Convert $4$ to decimal.

$y = 4$

Step 3

Find the point at $x = 5$ .

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Step 3.1

Replace the variable $x$ with $5$ in the expression.

$f (5) = \frac{{((5) - 3)}^{3} + 16}{4}$

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

Subtract $3$ from $5$ .

$f (5) = \frac{2^{3} + 16}{4}$

Step 3.2.1.2

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

$f (5) = \frac{8 + 16}{4}$

Step 3.2.1.3

Add $8$ and $16$ .

$f (5) = \frac{24}{4}$

Step 3.2.2

Divide $24$ by $4$ .

$f (5) = 6$

Step 3.2.3

The final answer is $6$ .

$6$

Step 3.3

Convert $6$ to decimal.

$y = 6$

Step 4

Find the point at $x = 2$ .

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Step 4.1

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

$f (2) = \frac{{((2) - 3)}^{3} + 16}{4}$

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

Subtract $3$ from $2$ .

$f (2) = \frac{{(- 1)}^{3} + 16}{4}$

Step 4.2.1.2

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

$f (2) = \frac{- 1 + 16}{4}$

Step 4.2.1.3

Add $- 1$ and $16$ .

$f (2) = \frac{15}{4}$

Step 4.2.2

The final answer is $\frac{15}{4}$ .

$\frac{15}{4}$

Step 4.3

Convert $\frac{15}{4}$ to decimal.

$y = 3.75$

Step 5

Find the point at $x = 4$ .

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Step 5.1

Replace the variable $x$ with $4$ in the expression.

$f (4) = \frac{{((4) - 3)}^{3} + 16}{4}$

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

Subtract $3$ from $4$ .

$f (4) = \frac{1^{3} + 16}{4}$

Step 5.2.1.2

One to any power is one.

$f (4) = \frac{1 + 16}{4}$

Step 5.2.1.3

Add $1$ and $16$ .

$f (4) = \frac{17}{4}$

Step 5.2.2

The final answer is $\frac{17}{4}$ .

$\frac{17}{4}$

Step 5.3

Convert $\frac{17}{4}$ to decimal.

$y = 4.25$

Step 6

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

$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & 3.75 \\ 3 & 4 \\ 4 & 4.25 \\ 5 & 6 \end{array}$

Step 7

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

Rises to the left and rises to the right

$\begin{array}{c} x & y \\ 1 & 2 \\ 2 & 3.75 \\ 3 & 4 \\ 4 & 4.25 \\ 5 & 6 \end{array}$

Step 8