Question

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

Answer 1

Answer: f(x) = log(1/x), x ≠ 0.

Reason: pH = −log10[H+] = log10(1/[H+]). For x = 1/10, log(1/(1/10)) = log(10) = 1; for x = 1/100, log(100) = 2, etc., matching the table.