Question

Which statement is true about the discontinuities of the function f(x)? F (x) = StartFraction x minus 5 Over 3 x squared minus 17 x minus 28 EndFraction

Answer 1

Question:

Which statement is true about the discontinuities of the function $f(x) = \frac{x-5}{3x^2-17x-28}$

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 .

Answer:

B)There are asymptotes at x = 7 and $(x = \frac{-4}{3})$

Step-by-step explanation:

Given:

$f(x) = \frac{x-5}{3x^2-17x-28}$

Required:

Find the true statement

$f(x) = \frac{x-5}{3x^2-17x-28}$

We'll first factorize the denominator.

$f(x) = \frac{x-5}{(3x+4)(x-7)}$

Make x subject of the formula in (3x+4) and (x-7):

3x + 4 =

3x = -4

Divide both sides by 3:

$x = \frac{-4}{3}$

x - 7

x = 7

Now check for the limit when $(x = \frac{-4}{3})$ and (x = 7)

lim f(x) when   $(x = \frac{-4}{3})$ = ±∞

lim f(x) when (x=7) = ±∞

Sinve they both make the denominator tend to zero, they are asymptotes

Therefore, there are asymptotes at $(x = \frac{-4}{3})$ and x=7

Option B is correct