Step-by-step explanation:
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A vertical asymptote is what you get when you try to divide by 0. To find where you get these, you need to look at the denominator and what values of x will make the denominator equal to 0.
In your denominator, you have (x+7)(x-5)(x-3).
What values of x makes (x+7)(x-5)(x-3)=0?
If x = -7, if x = 5, or if x = 3, then that entire expression will equal zero. (Same idea as when you solve equations by factoring.
Now the only place this can get trickier is if one of those factors — one of (x+7), (x-5), or (x-3) — also appears in the numerator. If that happens, then it’s more involved whether you have an asymptote or not. But that doesn’t happen in this example.
So the short version: Asymptotes happen when you try to divide by zero. Dividing by zero is not a good thing. So you just ask yourself, “What will make the denominator 0?”
Given:
Triangle ABC with vertices A (-1, 4), B( -4, 1), and C(-1, 1) is reflected across the y-axis and then translated 4 units to the left to form triangle A’B’C’.
To find:
The coordinates of the vertices of triangle A’B’C’.
Solution:
If triangle ABC reflected across y-axis, then
Coordinates of image after reflection across y-axis are 
Then triangle translated 4 units to the left to form triangle A’B’C’.
Therefore, the vertices of triangle A’B’C’ are A’ (-3, 4), B’ (0, 1), C’ (-3, 1).
Hence, the correct option is B.
I am pretty sure it's 82/100.
From the Figure :
Point A is (-3 , -3)
Point B is (6 , 6)
We know that, The Mid Point of Two Points (x₁ , y₁) and (x₂ , y₂) is given by :
![\mathsf{\implies [(\frac{x_1 + x_2}{2})\;,\;(\frac{y_1 + y_2}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20%5B%28%5Cfrac%7Bx_1%20%2B%20x_2%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7By_1%20%2B%20y_2%7D%7B2%7D%29%5D%7D)
![\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{-3 + 6}{2})\;,\;(\frac{-3 + 6}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Midpoint%5C%3Bof%5C%3BLine%5C%3BAB%5C%3Bis%5C%3B%5B%28%5Cfrac%7B-3%20%2B%206%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7B-3%20%2B%206%7D%7B2%7D%29%5D%7D)
![\mathsf{\implies Midpoint\;of\;Line\;AB\;is\;[(\frac{3}{2})\;,\;(\frac{3}{2})]}](https://tex.z-dn.net/?f=%5Cmathsf%7B%5Cimplies%20Midpoint%5C%3Bof%5C%3BLine%5C%3BAB%5C%3Bis%5C%3B%5B%28%5Cfrac%7B3%7D%7B2%7D%29%5C%3B%2C%5C%3B%28%5Cfrac%7B3%7D%7B2%7D%29%5D%7D)
