Question

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

y = (x-7)(x-3) / x^2-10x+21

A. x = 1, x = –8, x = –2; yes
B. x = 7, x = 3; yes
C. x = –7, x = –3; no
D. x = –1, x = 8, x = 2; no

Answer 1

The answer would be B.

Answer 2

factor

`((x-7)(x-3))/((x-7)(x-3)) =1`
it simplifies to y=1
(x-7)(x-3)
they are undefined since they make the denomenator 0
solve
(x-7)(x-3)=0
x-7=0
x=7
x-3=0
x=3
restricted values are x=3 and x=7
but, the points x=3 and x=7 are holes since they were canceled out

answer is B