Finite Math Examples

$y = (\frac{1}{x}) + 3$

Step 1

Find the x-intercepts.

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Step 1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = (\frac{1}{x}) + 3$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{x} + 3 = 0$ .

$\frac{1}{x} + 3 = 0$

Step 1.2.2

Subtract $3$ from both sides of the equation.

$\frac{1}{x} = - 3$

Step 1.2.3

Find the LCD of the terms in the equation.

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Step 1.2.3.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$x, 1$

Step 1.2.3.2

The LCM of one and any expression is the expression.

$x$

Step 1.2.4

Multiply each term in $\frac{1}{x} = - 3$ by $x$ to eliminate the fractions.

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Step 1.2.4.1

Multiply each term in $\frac{1}{x} = - 3$ by $x$ .

$\frac{1}{x} x = - 3 x$

Step 1.2.4.2

Simplify the left side.

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Step 1.2.4.2.1

Cancel the common factor of $x$ .

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Step 1.2.4.2.1.1

Cancel the common factor.

$\frac{1}{x} x = - 3 x$

Step 1.2.4.2.1.2

Rewrite the expression.

$1 = - 3 x$

Step 1.2.5

Solve the equation.

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Step 1.2.5.1

Rewrite the equation as $- 3 x = 1$ .

$- 3 x = 1$

Step 1.2.5.2

Divide each term in $- 3 x = 1$ by $- 3$ and simplify.

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Step 1.2.5.2.1

Divide each term in $- 3 x = 1$ by $- 3$ .

$\frac{- 3 x}{- 3} = \frac{1}{- 3}$

Step 1.2.5.2.2

Simplify the left side.

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Step 1.2.5.2.2.1

Cancel the common factor of $- 3$ .

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Step 1.2.5.2.2.1.1

Cancel the common factor.

$\frac{- 3 x}{- 3} = \frac{1}{- 3}$

Step 1.2.5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{- 3}$

Step 1.2.5.2.3

Simplify the right side.

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Step 1.2.5.2.3.1

Move the negative in front of the fraction.

$x = - \frac{1}{3}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{3}, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = (\frac{1}{0}) + 3$

Step 2.2

The equation has an undefined fraction.

Undefined

Step 2.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 3

List the intersections.

x-intercept(s): $(- \frac{1}{3}, 0)$

y-intercept(s): $None$

Step 4