# Chapter 2 - Nonlinear Functions - 2.3 Polynomial and Rational Functions - 2.3 Exercises - Page 74: 16

$$y=\frac{2x^{2}+3}{x^{2}-1}$$ The values $x= \pm 1$ makes the denominator 0, but not the numerator, so the lines with equations $$x=1 , \, x=-1$$ as vertical asymptotic. To find a horizontal asymptotic, let $x$ get larger and larger, so that $2x^{2}+3 \approx 2x^{2}$ because the 3 is very small compared with $2x^{2}$. Similarly, for $x$ very large $x^{2}-1 \approx x^{2}$ . Therefore, $$y=\frac{2x^{2}+3}{x^{2}-1} \approx \frac{2x^{2}}{x^{2}} \approx 2.$$ This means that the line $y=2$ is a horizontal asymptotic. When $x=0$ the y-intercept is -3 This is graph $B$. $$y=\frac{2x^{2}+3}{x^{2}-1}$$ The values $x= \pm 1$ makes the denominator 0, but not the numerator, so the lines with equations $$x=1 , \, x=-1$$ as vertical asymptotic. To find a horizontal asymptotic, let $x$ get larger and larger, so that $2x^{2}+3 \approx 2x^{2}$ because the 3 is very small compared with $2x^{2}$. Similarly, for $x$ very large $x^{2}-1 \approx x^{2}$ . Therefore, $$y=\frac{2x^{2}+3}{x^{2}-1} \approx \frac{2x^{2}}{x^{2}} \approx 2.$$ This means that the line $y=2$ is a horizontal asymptotic. When $x=0$ the y-intercept is -3 This is graph $B$. 