Calculus Examples

$y = \frac{7 x^{2} - 7}{x^{3}}$

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 $x$ .

$0 = \frac{7 x^{2} - 7}{x^{3}}$

Step 1.2

Solve the equation.

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Step 1.2.1

Set the numerator equal to zero.

$7 x^{2} - 7 = 0$

Step 1.2.2

Solve the equation for $x$ .

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Step 1.2.2.1

Add $7$ to both sides of the equation.

$7 x^{2} = 7$

Step 1.2.2.2

Divide each term in $7 x^{2} = 7$ by $7$ and simplify.

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Step 1.2.2.2.1

Divide each term in $7 x^{2} = 7$ by $7$ .

$\frac{7 x^{2}}{7} = \frac{7}{7}$

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.

$\frac{7 x^{2}}{7} = \frac{7}{7}$

Step 1.2.2.2.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{7}{7}$

Step 1.2.2.2.3

Simplify the right side.

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Step 1.2.2.2.3.1

Divide $7$ by $7$ .

$x^{2} = 1$

Step 1.2.2.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{1}$

Step 1.2.2.4

Any root of $1$ is $1$ .

$x = \pm 1$

Step 1.2.2.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.2.2.5.1

First, use the positive value of the $\pm$ to find the first solution.

$x = 1$

Step 1.2.2.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 1$

Step 1.2.2.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$x = 1, - 1$

Step 1.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 1, 0)$

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 $y$ .

$y = \frac{7 {(0)}^{2} - 7}{{(0)}^{3}}$

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): $(1, 0), (- 1, 0)$

y-intercept(s): $None$

Step 4