Find a formula for a function f that satisfies the following conditions. lim x→±∞ f(x) = 0,   lim x→0 f(x) = −∞,  f(2) = 0 lim x→7− f(x) = ∞,   lim x→7+ f(x ) = −∞​

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  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))

1.3

step-by-step explanation:

3x2=6   9x+6

bring down the 6 on both sides

6+6=12

12= 9x

divide by 9

12/9 =

1.3 =x