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 ) = −∞​

9514 1404 393

  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))

may i see the picture? it would a lot, xox

3

step-by-step explanation: