Question

Find any points of discontinuity for the rational function.What are the points of discontinuity? Are they all removable?

Answer 1

so what you do is find any vertical assemtotes and holes

VA's are the factors of the denomenator
holes are the factors that cancel from top and bottom


so
factor bottom
(x-3)(x-7)

we get
y=[(x-7)(x-3)]/[(x-7)(x-3)]
simplifying to
y=1

we notice that factored out x-7 and x-3

set them to zero
x-7=0
x=7

x-3=0
x=3

at x=7 and x=3 there are holes

they are gaps or holes there and it is removable because you could graph y=1 and get the same graph except for those removed points


the points are at (7,1) and (3,1)