Precalculus Examples

$\frac{x - 4}{x^{2} - 16}$

Step 1

Write $\frac{x - 4}{x^{2} - 16}$ as an equation.

$y = \frac{x - 4}{x^{2} - 16}$

Step 2

Find the x-intercepts.

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Step 2.1

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

$0 = \frac{x - 4}{x^{2} - 16}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$x - 4 = 0$

Step 2.2.2

Add $4$ to both sides of the equation.

$x = 4$

Step 2.2.3

Exclude the solutions that do not make $0 = \frac{x - 4}{x^{2} - 16}$ true.

$No solution$

Step 2.3

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

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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Step 3.1

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

$y = \frac{(0) - 4}{{(0)}^{2} - 16}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{0 - 4}{{(0)}^{2} - 16}$

Step 3.2.2

Remove parentheses.

$y = \frac{0 - 4}{0^{2} - 16}$

Step 3.2.3

Remove parentheses.

$y = \frac{(0) - 4}{{(0)}^{2} - 16}$

Step 3.2.4

Simplify $\frac{(0) - 4}{{(0)}^{2} - 16}$ .

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Step 3.2.4.1

Subtract $4$ from $0$ .

$y = \frac{- 4}{0^{2} - 16}$

Step 3.2.4.2

Simplify the denominator.

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Step 3.2.4.2.1

Raising $0$ to any positive power yields $0$ .

$y = \frac{- 4}{0 - 16}$

Step 3.2.4.2.2

Subtract $16$ from $0$ .

$y = \frac{- 4}{- 16}$

Step 3.2.4.3

Cancel the common factor of $- 4$ and $- 16$ .

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Step 3.2.4.3.1

Factor $- 4$ out of $- 4$ .

$y = \frac{- 4 (1)}{- 16}$

Step 3.2.4.3.2

Cancel the common factors.

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Step 3.2.4.3.2.1

Factor $- 4$ out of $- 16$ .

$y = \frac{- 4 \cdot 1}{- 4 \cdot 4}$

Step 3.2.4.3.2.2

Cancel the common factor.

$y = \frac{- 4 \cdot 1}{- 4 \cdot 4}$

Step 3.2.4.3.2.3

Rewrite the expression.

$y = \frac{1}{4}$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{4})$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, \frac{1}{4})$

Step 5