find the vertical asymptote.\n\n$$y = \\frac{2x - 8}{x + 4}$$\n\n$$x = ?$$

Explanation:

Step1: Identify the denominator of the rational function

The given function is $y = \frac{2x - 8}{x + 4}$. The denominator is $x + 4$.

Step2: Set the denominator equal to zero

Vertical asymptotes occur where the denominator is zero and the numerator is non-zero. $$x + 4 = 0$$

Step3: Solve for x

Subtract 4 from both sides of the equation. $$x = -4$$

Step4: Verify the numerator is non-zero

Substitute $x = -4$ into the numerator $2x - 8$. $$2(-4) - 8 = -8 - 8 = -16$$ Since $-16 \neq 0$, $x = -4$ is a vertical asymptote.

Answer:

x = -4