# Betty is training by swimming lengths of a 50-m pool at a constant speed. SHe swims one length every minute.A) graph her distance. In metres, from her startig point versus the time, in minutes, for...

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(a) Betty is at the starting point at time t=0, and is 50m away at time t=1 min, she is back at her starting point at time t=2 min, etc... She is swimming at a constant rate, so the function is linear.

The graph:

(b) The period is the amount of time it takes for the function to repeat itself.(Note that this only applies to periodic (repeating) functions; hence the name). One way to determine the period is to measure the distance between corresponding parts of the graph;i.e. the distance between peaks or the distance between troughs, etc...

**In this case the period is 2min.**

(The frequency is 1 repetition every 2 min: the period is the reciprocal of the frequency. Thus if your electricity is delivered at a frequency of 60 hertz (cycles per second), then the period is 1/60 seconds)

The amplitude is the distance of a peak or trough from the midline, or the maximum minus the minimum divided by 2.

**Here, the amplitude is `(50-0)/2=25` meters.**

(c) The domain is all possible inputs; here the input is the time and we are restricted to the first 6 minutes, **so the domain is [0,6],measured in minutes.**

The range runs from the minimum to the maximum of the outputs, **so the range is [0,50], measured in meters**.