A science teacher wrote the table of values below. Amount of Hydrogen vs. pH Amount of Hydrogen, x (in moles per liter) pH, f(x) One-tenth 1 StartFraction 1 Over 100 EndFraction 2 StartFraction 1 Over 1000 EndFraction 3 StartFraction 1 Over 10,000 EndFraction 4 StartFraction 1 Over 100,000 EndFraction 5 Which function models the data in the table? f (x) = StartFraction 1 Over x EndFraction, x not-equals 0 f (x) = log StartFraction 1 Over x squared EndFraction, x not-equals 0 f (x) = log StartFraction 1 Over x EndFraction, x not-equals 0 f (x) = StartFraction 1 Over x squared EndFraction, x not-equals 0

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AFOKE88 AFOKE88 · Answer 1 · 2022-06-17T17:31:23+02:00

The function that represents the values in the given table is; f(x) = log (1/x ), x ≠ 0

From the attached table, we see that;

If x = 1/10, then f(x) = 1

From logarithm rule;

log(10) = 1

log(100) = 2

For the function f(x) = log (1/x), we have;

when;

x = 1/10, we have;

f(x) = log (1/(1/10)) = log (10) = 1

If x = 1/100, then;

f(x) = log (1/(1/100)) = log (100) = 2

Thus, the final answer is;

f(x) = log (1/x ), x ≠ 0

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