Tonya plans to join a fitness club. She researched the costs to join different clubs in her area and found that there is a linea
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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 .
Answer:
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