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

d) by the cross product property, ab^2 = bc multiplied by ad

step-by-step explanation:

we are given

in the given triangle abc

angle a is 90° and segment ad is perpendicular to segment bc

we can see that

triangle(abc) and triangle(abd) are similar because they have common side and same angle (90 degree)

so, triangles(abc) and abd are similar

since, they are similar

so, the ratio of their sides must be equal

we get

now, we can cross multiply

and we get

so, this could be step to prove it