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

Asked by maham237 @ in Mathematics viewed by 870 People

Which statement is true about the discontinuities of the function f(x) = x-5/3x^2-17x-28
A)There are holes at x = 7 and .
B)There are asymptotes at x = 7 and .
C)There are asymptotes at x = –7 and .
D)There are holes at (–7, 0) and .

Answered by maham237 @


1) function f(x)

x - 5
f(x) = ----------------
3x^2 - 17x - 28

2) factor the denominator:

3x^2 - 17x - 28 = (3x + 4)(x - 7)

x - 5
=> f(x) = -----------------------
(3x + 4) (x - 7)

3) Find the limits when x → - 4/3 and when x → 7

Lim of f(x) when x → - 4/3 = +/- ∞

=> vertical assymptote x = - 4/3

Lim of f(x) when x → 7 = +/- ∞

=> vertical assymptote x = 7

Answer: there are assympotes at x = 7 and x = - 4/3

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