Question 1140740
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(1) The period is how much the x value changes from the beginning of one cycle to the beginning of the next.  One way to see a complete cycle is to go from one maximum to the next maximum.  In the figure, there are maxima at x=0, x=4, and x=8.  Use that to answer this part of the problem.<br>
(2) The range is the set of y values that the function takes on.  For example, if the smallest value a function takes on is -3 and the largest value is 11, the range is from -3 to 11, often written as [-3,11].<br>
What are the smallest and largest y values for this function?<br>
(3) The domain is the set of x values (or, in this case, t values) that the function can take on.  The smallest t value in the graph is 0 (which makes sense, since t represents time; the scientist couldn't have started the experiment at a negative time).<br>
You found the period in step (1); how long after t=0 is the end of 20 periods?<br>
(4) The axis (or center line) is the horizontal line about which the function value oscillates.  Since it is a horizontal line, the equation will be y=c for some constant value c.  That value is the number in the exact middle of the range.  So use your answer for (2) to get the equation of the axis.<br>
(5) The amplitude is the difference between the y value of the axis and the y value of the maximum or minimum.  You have both of those numbers from earlier parts of the problem.