Which statement is true about the discontinuities of the function f (x) ?

f (x) = StartFraction x + 1 Over 6 x squared minus 7 x minus 3 EndFraction

There are asymptotes at x = three-halves and x = negative one-third.

There are holes at x = three-halves and x = negative one-third.

There are asymptotes at x = negative three-halves and x = one-third.

There are holes at x = negative three-halves and x = one-third.

Question

Mathematics

Gustavo Murphy

13 February, 12:19

Which statement is true about the discontinuities of the function f (x) ?

f (x) = StartFraction x + 1 Over 6 x squared minus 7 x minus 3 EndFraction

There are asymptotes at x = three-halves and x = negative one-third.

There are holes at x = three-halves and x = negative one-third.

There are asymptotes at x = negative three-halves and x = one-third.

There are holes at x = negative three-halves and x = one-third.

+4

Answers (1)

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Ali Paul · Answer 1

There are asymptotes at x = three-halves and x = negative one-third.

Step-by-step explanation:

f (x) = (x + 1) / (6x^2 - 7x - 3)

= (x + 1) ( / (6x^2 + 2x - 9x - 3)

= (x + 1) / (2x (3x + 1) - 3 (3x + 1))

= (x + 1) / (2x - 3) (3x + 1)

Now x = 3/2 and x = - 1/3 both make te denominator zero so these are both asymptotes.