Question 1119800: Which of the following is the general symbolic form of a square root function?
A.f(x)= x√a+b
B.f(x)= x+√a
C.f(x)= x√a+b
D.f(x)= √x-a+B
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Which of the following is the general symbolic form of a rational function
A.f(x)=√ax+b
B.f(x)=(1)/(x-b)+c
C.f(x)=mx+b
D.f(x)=1+(x)/(b-a)
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Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
These questions cannot be answered definitively. The "general symbolic form of a square root function" and the "general symbolic form of a rational function" are things for which there is not a universally accepted answer. The answers will depend on the textbook or other resource you are using.
In terms of transformations of "parent" functions, there are examples such as
y = a|x-h|+k for an absolute value function and
y = a(x-h)^2+k for a quadratic function.
So if we go by those examples, the best answer choices for your two questions are
square root: y = sqrt(x-a)+b which I think is your answer choice D
and
rational function: y = 1/(x-b)+c which is your answer choice B
However, neither of those is a really good "general form".
Answer choice D for the square root has a horizontal shift and a vertical shift; but it lacks a vertical stretch.
Answer choice B for the rational function is the same -- it has a horizontal shift and a vertical shift but no vertical stretch.
And furthermore it is a general form of the simplest form of a rational function, involving a single linear polynomial in the denominator. A rational function can be ANY function in the form of a fraction with any polynomial(s) in the numerator and denominator.
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