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

Ax = 1, x = –8, x = –2; yes
Bx = 7, x = 3; yes
Cx = –7, x = –3; no
Dx = –1, x = 8, x = 2; no

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24-11-2016
Mathematics

Answered

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

Ax = 1, x = –8, x = –2; yes
Bx = 7, x = 3; yes
Cx = –7, x = –3; no
Dx = –1, x = 8, x = 2; no

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apologiabiology apologiabiology · Answer 1 · 2016-11-24T00:17:16-05:00

apologiabiology apologiabiology

24-11-2016

factor
\(\frac{(x-7)(x-3)}{(x-7)(x-3)} =1\)
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

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syed514 syed514 · Answer 2 · 2016-11-25T12:12:19-05:00

syed514 syed514

25-11-2016

The answer would be B.

Answer Link

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 Ax = 1, x = –8, x = –2; yes Bx = 7, x = 3; yes Cx = –7, x = –3; no Dx = –1, x = 8, x = 2; no

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Related Questions

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

Ax = 1, x = –8, x = –2; yes
Bx = 7, x = 3; yes
Cx = –7, x = –3; no
Dx = –1, x = 8, x = 2; no