What function remains when the frequency is zero? Does it have a least positive period?
- Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons
Working and explanation
BUILD THE REASONING
Hint 1
Separate amplitude, internal frequency, phase and vertical shift.
Hint 2
Every positive shift preserves a constant function.
Worked solution
Separate amplitude, internal frequency, phase and vertical shift.
Calculate or simplify this relation.
Because arbitrarily small positive shifts work, there is no least one.
The constant 7; it has no least positive period.
Checks and common pitfalls: Because arbitrarily small positive shifts work, there is no least one.
Reasoning checklist · self / teacher assessment
- State the relevant definition, condition or model.
- Show a valid calculation, proof or counterexample.
- Interpret the conclusion with its restrictions.
Think first. Reveal a hint when the class is ready.