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.

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

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

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.

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.