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Answer:
f(x) = (x -2)/(x²(7-x))
Step-by-step explanation:
The horizontal asymptotes of zero mean the denominator degree needs to be greater than the numerator degree. The zero at x=2 means (x-2) will be a factor in the numerator. The limit at x=0 means there will be a factor of x² in the denominator. Since the numerator term is negative at x=0, the signs of the terms so far do not need modification.
The vertical asymptote at x=7 means there will be a factor of (x-7) in the denominator. In order for the limits to be correct, it must have a negative sign:
-(x -7) = (7 -x)
Then the function with these characteristics can be written ...
f(x) = (x -2)/(x²(7 -x))
