Answer
(a) A rational function is a function containing two polynomials one being the numerator,
the other one being the denominator.
(b) $x = a$ is a vertical asymptote of $y=f(x)$ when $x\to a, f(x)\to-\infty$ or $\infty$.
(c) $y=b$ is a horizontal asymptote of $f(x)$ when $x\to\pm\infty$, $f(x)\to b$
(d) vertical asymptotes $x=-2,2$, horizontal asymptote $y=5$
Work Step by Step
(a) A rational function is a function containing two polynomials one being the numerator,
the other one being the denominator.
(b) $x = a$ is a vertical asymptote of $y=f(x)$ when x approaches a, $f(x)$ goes to $-\infty$ or $\infty$.
(c) $y=b$ is a horizontal asymptote of $f(x)$ when x approaches $\pm\infty$, $f(x)\to b$
(d) $f(x)=\frac{5x^2+3}{(x+2)(x-2)}$, vertical asymptotes $x=-2,2$, horizontal asymptote $y=5$
