Find the x and y Intercepts F(x)=(x+2)/(x^2-6x-16)

$F (x) = \frac{x + 2}{x^{2} - 6 x - 16}$

Step 1

Find the x-intercepts.

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

$0 = \frac{x + 2}{x^{2} - 6 x - 16}$

Solve the equation.

Set the numerator equal to zero.

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

Exclude the solutions that do not make $0 = \frac{x + 2}{x^{2} - 6 x - 16}$ true.

$No solution$

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.

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

$y = \frac{(0) + 2}{{(0)}^{2} - 6 \cdot 0 - 16}$

Solve the equation.

Remove parentheses.

$y = \frac{0 + 2}{{(0)}^{2} - 6 \cdot 0 - 16}$

Remove parentheses.

$y = \frac{0 + 2}{0^{2} - 6 \cdot 0 - 16}$

Remove parentheses.

$y = \frac{(0) + 2}{{(0)}^{2} - 6 \cdot 0 - 16}$

Simplify $\frac{(0) + 2}{{(0)}^{2} - 6 \cdot 0 - 16}$ .

Add $0$ and $2$ .

$y = \frac{2}{0^{2} - 6 \cdot 0 - 16}$

Simplify the denominator.

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

$y = \frac{2}{0 - 6 \cdot 0 - 16}$

Multiply $- 6$ by $0$ .

$y = \frac{2}{0 + 0 - 16}$

Add $0$ and $0$ .

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

Subtract $16$ from $0$ .

$y = \frac{2}{- 16}$

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ and $- 16$ .

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 16}$

Cancel the common factors.

Factor $2$ out of $- 16$ .

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 8}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

Find the x and y Intercepts F(x)=(x+2)/(x^2-6x-16)

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