Calculus Examples

$f (x) = \frac{1}{x^{2} + 2 x - 8}$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

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

$0 = \frac{1}{x^{2} + 2 x - 8}$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Set the numerator equal to zero.

$1 = 0$

Step 1.2.2

Since $1 \neq 0$ , there are no solutions.

No solution

Step 1.3

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

x-intercept(s): $None$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

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

$y = \frac{1}{{(0)}^{2} + 2 (0) - 8}$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Remove parentheses.

$y = \frac{1}{0^{2} + 2 (0) - 8}$

Step 2.2.2

Remove parentheses.

$y = \frac{1}{{(0)}^{2} + 2 (0) - 8}$

Step 2.2.3

Simplify $\frac{1}{{(0)}^{2} + 2 (0) - 8}$ .

Tap for more steps...

Step 2.2.3.1

Simplify the denominator.

Tap for more steps...

Step 2.2.3.1.1

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

$y = \frac{1}{0 + 2 (0) - 8}$

Step 2.2.3.1.2

Multiply $2$ by $0$ .

$y = \frac{1}{0 + 0 - 8}$

Step 2.2.3.1.3

Add $0$ and $0$ .

$y = \frac{1}{0 - 8}$

Step 2.2.3.1.4

Subtract $8$ from $0$ .

$y = \frac{1}{- 8}$

Step 2.2.3.2

Move the negative in front of the fraction.

$y = - \frac{1}{8}$

Step 2.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{8})$

Step 3

List the intersections.

x-intercept(s): $None$

y-intercept(s): $(0, - \frac{1}{8})$

Step 4