99 points, pre calculus and limits question.
identify the functions that exhibit a jump discontinuity.

There is a jump discontinuity if the graph approaches a differnt value as you approach from a differnt side

so it would be like piecewise function
y=x+1 for x<1 and
y=x+3 for x≤1

the first function approaches 2 but the 2nd one approaches 4, so they do not approach the same value and therefor jump
the easiest way is to evaluate the function for that value that they approach

so

f(x)
using 9 for x in the fraction thing, we get -4/(277)
for the bottom one we get 142
they do not approach the same number so it is a jump discontinuty

g(x)
for x=4, the quadratic equation approaches 18
for both of them
no jump discontinuity

h(x)
for the cubic function, it spproaches 144
for the linear fuction is approaches 144
no jump discontinuity

i(x)
cubic function, it appraoches 25
liner function appraoches 25
no jump discinouity

j(x)
quadratic one appraohces 144
bottom one approahcesr 143
jump discontinuity yes

bottom i(x)
linear one approaches 22
bottom one approahces 21
jump disconintuity

so the one that jump are

f(x), j(x) and the bottom i(x)

Ithink it is15not sure tho