Final answer:
The concept of a zero with a multiplicity of 3 applies to polynomial functions, where a zero repeats as a root three times. Trigonometric, exponential, and logarithmic functions do not exhibit this behavior.
Step-by-step explanation:
The question asks which functions can have a zero with a multiplicity of 3. A zero of multiplicity 3 means that the zero repeats three times as a root of the function's equation. This concept is most commonly applicable to polynomial functions, where a factor of the form (x - a) is raised to the power of three, indicating that x = a is a root with multiplicity 3.
For instance, if a polynomial has a factor (x - 2)3, it means that x = 2 is a root with multiplicity 3. Trigonometric functions, logarithmic functions, and exponential functions do not have zeros with multiplicities in the same sense as polynomials because their zeroes do not occur as repeated factors in an equation. Trigonometric functions like sine and cosine have periodic zeros but not in the multiplicity context, while exponential functions do not cross the x-axis, hence they don't have real zeros. Logarithmic functions are undefined at zero and cannot approach zero from the negative side, so they cannot have a zero, let alone one of a specific multiplicity.