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...

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 six lengths of the pool. B) Determine the period and amplitude of the function. C) state the domain and range. Please explain what a period and amplitde is. Thanks

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embizze | High School Teacher | (Level 1) Educator Emeritus

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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.

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