Answer:
![g(x)=\sqrt[3]{x-3}+4](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%5B3%5D%7Bx-3%7D%2B4)
Step-by-step explanation:
The function g(x) is a shifted version of the function f(x); f(x) is shifted by 3 along x-axis and by 4 along y-axis.
Another way of thinking about this is that the function g(x) contains points (3, 4); therefore,
which goes through the point (3, 4).
Answer:
Step-by-step explanation:
We can rewrite the equation as
Notice that we have 
in both the numerator and the denominator, so it looks like we can divide it out. However, what if is 
? Then we would have 
, which is undefined. So although it looks like the numerator and denominator can be simplified, the resulting function we would get from simplification would not have the same behavior as this one (since such a function would be defined for 
, but this one is not).
A point of discontinuity refers to a particular point which is included in the simplified function, but which is not included in the original one. In this case, the point which is not included in the unsimplified function is at . In the simplified version of the function, if we plug in , we get
So the point is our only point of discontinuity.
It's also important to distinguish between specific points of discontinuity and vertical asymptotes. This function also has a vertical asymptote at 
(since it causes the denominator to be 0), but the difference in behavior is that in the case of the asymptote, only the denominator becomes 0 for a specific value of 
<h3>
Answer: B) 7 units</h3>
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Explanation:
The y coordinates of the two points are the same, so we can subtract the x coordinates and apply absolute value
|R - T| = |-6 - 1| = |-7| = 7
Or we can say
|T - R| = |1 - (-6)| = |1 + 6| = |7| = 7
Either way, the two points are 7 units apart.
You could use the distance formula to get the same answer, but that's definitely overkill in my opinion. The trick mentioned above also could work if the x coordinates were the same, but the y coordinates were different. In any other case, you would have to use the distance formula.
It would be 4!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
