identify the discontinuous functions and arrange them according to the positions of their points of infinite…

Explanation:

Step1: Find points of infinite - discontinuity

For a rational function $y = \frac{p(x)}{q(x)}$, points of infinite discontinuity occur where $q(x)=0$. For $f(x)=\frac{x^{2}+2x - 63}{x + 7}$, set $x+7 = 0$, then $x=-7$. For $g(x)=\frac{x^{2}-2x - 35}{x - 5}$, set $x - 5=0$, then $x = 5$. For $h(x)=\frac{x^{2}+6x - 55}{x - 11}$, set $x - 11=0$, then $x = 11$. For $i(x)=\frac{x^{2}-11x - 42}{x + 4}$, set $x + 4=0$, then $x=-4$. For $j(x)=\frac{x^{2}+4x}{x - 2}$, set $x - 2=0$, then $x = 2$. For $k(x)=\frac{x^{2}-3x - 54}{x - 9}$, set $x - 9=0$, then $x = 9$. For $l(x)=\frac{x^{2}+8x + 12}{x^{2}+2}$, since $x^{2}+2>0$ for all real $x$, there are no points of infinite - discontinuity. For $m(x)=\frac{x^{2}-4x - 96}{x - 8}$, set $x - 8=0$, then $x = 8$.

Step2: Arrange the points

The points of infinite discontinuity are $x=-7,x=-4,x = 2,x = 5,x = 8,x = 9,x = 11$. Arranging from the farthest left to the farthest right: $f(x),i(x),j(x),g(x),m(x),k(x),h(x)$

Answer:

$f(x),i(x),j(x),g(x),m(x),k(x),h(x)$