Rational Functions and Zeros Practice Test

A rational function is a quotient of polynomials. For $f(x)=\dfrac{x^2-4}{x-2}$, zeros occur where $f(x)=0$ and the function is defined; vertical asymptotes come from non-canceling denominator zeros. Since $x^2-4=(x-2)(x+2)$, the function behaves like $x+2$ except at $x=2$, where it is undefined. Based on the function described, which statement best describes the behavior at its zero?

A rational function is a quotient of two polynomials. For $f(x)=\dfrac{x^2-4}{x-2}$, zeros satisfy $f(x)=0$, and vertical asymptotes typically occur where the denominator is zero. Since $x^2-4=(x-2)(x+2)$, the factor $(x-2)$ cancels, leaving a removable discontinuity at $x=2$ (a hole), not a vertical asymptote. Based on the function described, determine the vertical asymptotes of $f(x)=\dfrac{x^2-4}{x-2}$.