Finite Math Examples

$f (x) = \frac{1}{7} \cdot {(x + 1)}^{2} - 5$

Step 1

Simplify $f (x)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$f (x) = \frac{1}{7} \cdot ((x + 1) (x + 1)) - 5$

Step 1.1.2

Expand $(x + 1) (x + 1)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$f (x) = \frac{1}{7} \cdot (x (x + 1) + 1 (x + 1)) - 5$

Step 1.1.2.2

Apply the distributive property.

$f (x) = \frac{1}{7} \cdot (x \cdot x + x \cdot 1 + 1 (x + 1)) - 5$

Step 1.1.2.3

Apply the distributive property.

$f (x) = \frac{1}{7} \cdot (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 5$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply $x$ by $x$ .

$f (x) = \frac{1}{7} \cdot (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 5$

Step 1.1.3.1.2

Multiply $x$ by $1$ .

$f (x) = \frac{1}{7} \cdot (x^{2} + x + 1 x + 1 \cdot 1) - 5$

Step 1.1.3.1.3

Multiply $x$ by $1$ .

$f (x) = \frac{1}{7} \cdot (x^{2} + x + x + 1 \cdot 1) - 5$

Step 1.1.3.1.4

Multiply $1$ by $1$ .

$f (x) = \frac{1}{7} \cdot (x^{2} + x + x + 1) - 5$

Step 1.1.3.2

Add $x$ and $x$ .

$f (x) = \frac{1}{7} \cdot (x^{2} + 2 x + 1) - 5$

Step 1.1.4

Apply the distributive property.

$f (x) = \frac{1}{7} x^{2} + \frac{1}{7} \cdot (2 x) + \frac{1}{7} \cdot 1 - 5$

Step 1.1.5

Simplify.

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Step 1.1.5.1

Combine $\frac{1}{7}$ and $x^{2}$ .

$f (x) = \frac{x^{2}}{7} + \frac{1}{7} \cdot (2 x) + \frac{1}{7} \cdot 1 - 5$

Step 1.1.5.2

Multiply $\frac{1}{7} (2 x)$ .

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Step 1.1.5.2.1

Combine $2$ and $\frac{1}{7}$ .

$f (x) = \frac{x^{2}}{7} + \frac{2}{7} x + \frac{1}{7} \cdot 1 - 5$

Step 1.1.5.2.2

Combine $\frac{2}{7}$ and $x$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1}{7} \cdot 1 - 5$

Step 1.1.5.3

Multiply $\frac{1}{7}$ by $1$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1}{7} - 5$

Step 1.2

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1}{7} - 5 \cdot \frac{7}{7}$

Step 1.3

Combine $- 5$ and $\frac{7}{7}$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1}{7} + \frac{- 5 \cdot 7}{7}$

Step 1.4

Combine the numerators over the common denominator.

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1 - 5 \cdot 7}{7}$

Step 1.5

Simplify the numerator.

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Step 1.5.1

Multiply $- 5$ by $7$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{1 - 35}{7}$

Step 1.5.2

Subtract $35$ from $1$ .

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} + \frac{- 34}{7}$

Step 1.6

Move the negative in front of the fraction.

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} - \frac{34}{7}$

Step 2

The word linear is used for a straight line. A linear function is a function of a straight line, which means that the degree of a linear function must be $0$ or $1$ . In this case, The degree of $f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} - \frac{34}{7}$ is $2$ , which makes the function a nonlinear function.

$f (x) = \frac{x^{2}}{7} + \frac{2 x}{7} - \frac{34}{7}$ is not a linear function