Precalculus Examples

$y = \frac{1}{x} - 5$

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 $x$ .

$0 = \frac{1}{x} - 5$

Step 1.2

Solve the equation.

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Step 1.2.1

Rewrite the equation as $\frac{1}{x} - 5 = 0$ .

$\frac{1}{x} - 5 = 0$

Step 1.2.2

Add $5$ to both sides of the equation.

$\frac{1}{x} = 5$

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 $\frac{1}{x} = 5$ by $x$ to eliminate the fractions.

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Step 1.2.4.1

Multiply each term in $\frac{1}{x} = 5$ by $x$ .

$\frac{1}{x} x = 5 x$

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.

$\frac{1}{x} x = 5 x$

Step 1.2.4.2.1.2

Rewrite the expression.

$1 = 5 x$

Step 1.2.5

Solve the equation.

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Step 1.2.5.1

Rewrite the equation as $5 x = 1$ .

$5 x = 1$

Step 1.2.5.2

Divide each term in $5 x = 1$ by $5$ and simplify.

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Step 1.2.5.2.1

Divide each term in $5 x = 1$ by $5$ .

$\frac{5 x}{5} = \frac{1}{5}$

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 $5$ .

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Step 1.2.5.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{1}{5}$

Step 1.2.5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{5}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{5}, 0)$

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 $y$ .

$y = \frac{1}{0} - 5$

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): $(\frac{1}{5}, 0)$

y-intercept(s): $None$

Step 4