Calculus Examples

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

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 $x$ .

$0 = \frac{7 x - 1}{x}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$7 x - 1 = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Add $1$ to both sides of the equation.

$7 x = 1$

Step 1.2.2.2

Divide each term in $7 x = 1$ by $7$ and simplify.

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Step 1.2.2.2.1

Divide each term in $7 x = 1$ by $7$ .

$\frac{7 x}{7} = \frac{1}{7}$

Step 1.2.2.2.2

Simplify the left side.

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Step 1.2.2.2.2.1

Cancel the common factor of $7$ .

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Step 1.2.2.2.2.1.1

Cancel the common factor.

$\frac{7 x}{7} = \frac{1}{7}$

Step 1.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{1}{7}$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{7}, 0)$

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 $y$ .

$y = \frac{7 (0) - 1}{0}$

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): $(\frac{1}{7}, 0)$

y-intercept(s): $None$

Step 4