# Question #eb249

##### 1 Answer

Domain:

Range:

Amplitude:

Period:

#### Explanation:

The domain is all the

The range is all the

The amplitude is how big the wave is (i.e. how far it goes from the x-axis).

The period is how long it takes for the wave to complete one cycle.

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Here is the graph of

graph{y=0.5sinx [-6.28, 6.28, -1, 1]}

Domain:

This graph goes on and on forever along the x axis, so you could pretty much plug in any value of

#x# and it would be defined.In mathematics, we would say that

#x# could be all real numbers, or for short,#x in RR# .

Range:

This isn't the same as domain. Notice that the curve only goes from

#-1/2# to#+1/2# . If you tried to find a point on the curve where the#y# -value was 2, for example, you couldn't do it, because 2 is outside the function'srange.Therefore, we would say that

#y# could be any number from#-1/2# to#1/2# . In mathematics we would write this as#-1/2 <= y <= 1/2# .

Amplitude:

This is actually answered by the last part; amplitude is just how far the wave travels from the x-axis at its furthest point. So, the amplitude for this particular wave is

#1/2# .

Period:

Let's say that one wave starts at

#0# . We need to find the point where the next wave starts.The wave goes above the x-axis, and crosses it again at

#x = pi# . Then, the wave goes below the x-axis, and finally comes back to its starting point at#x = 2pi# . Therefore, the period of the wave is#2pi# .