Define combined functions, Mathematics

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Q. Define Combined Functions?

Ans.

We are often interested in functions which combine a trigonometric function with another type of function.  For example, y = x + sinx with 0≤ x ≤ Π is the sum of two functions: y1 = x and y2 = sinx.

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To graph y = x + sinx, first draw y1 = x and y2 = x + sinx  on the same coordinate system.

2257_Combined Functions1.png

Now use a ruler or your eye to add the ordinates y1+y2 .

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Although some functions are easy to draw using addition of ordinates, combined functions can be very complicated to draw by hand.  In these cases, you should use a graphing calculator or other graphing utility to help you.

The graph of a product of two functions is found by  properties of the individual functions.

128_Combined Functions3.png

The graph of y = x + sinx  looks like a combination of the two functions y = x  and y = x + sinx .  The   part of the graph is bounded by the functions y= x  and y = - x.


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