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

Question:

Which statement is true about the discontinuities of the function

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 .

B)There are asymptotes at x = 7 and

Step-by-step explanation:

Given:

Required:

Find the true statement

We'll first factorize the denominator.

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

3x + 4 =

3x = -4

Divide both sides by 3:

x - 7

x = 7

Now check for the limit when and (x = 7)

lim f(x) when   = ±∞

lim f(x) when (x=7) = ±∞

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

Therefore, there are asymptotes at and x=7

Option B is correct

1. x> -5

2. x< 8

step-by-step explanation:

1. 2x> -10

divide by 2 from both sides of equation.

2x/2> -10/2

simplify, to find the answer.

-10/2=-5

x> -5 is the correct answer.

2. 3x< 24

divide by 3 from both sides of equation.

3x/3< 24/3

simplify, to find the answer.

24/3=8

x< 8 is the correct answer.

i hope this you, and have a wonderful day!

step-by-step explanation: