MediumMathematicsHigh School (11–12)Functions and Calculus › Graphs of FunctionsConceptualBoard Exam

Show that {x} = x - [x] has period 1. Then find the period of {5x}.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Show that $\{x\} = x - [x]$ has period $1$ . Then find the period of $\{5x\}$ .

Need a reminder? The key ideaShow

$|x - a| < r$ means $a - r < x < a + r$ . $[x]$ is the greatest integer not above $x$ , and $\{x\} = x - [x]$ lies in $[0, 1)$ . A piecewise function uses the rule for the piece that holds the input.

The worked solution

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Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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Show that {x} = x - [x] has period 1. Then find the period of {5x}.

The worked solution

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