SOLUTION: The function f is defined for 0 ≤ x ≤ 2pi, by f(x) = 3 + 5sin2x. State (i) the amplitude of f (ii) the period of f (iii) the maximum and minimum values of f (iv) Sketch the

Algebra ->  Test -> SOLUTION: The function f is defined for 0 ≤ x ≤ 2pi, by f(x) = 3 + 5sin2x. State (i) the amplitude of f (ii) the period of f (iii) the maximum and minimum values of f (iv) Sketch the      Log On


   

Question 1192196: The function f is defined for 0 ≤ x ≤ 2pi, by f(x) = 3 + 5sin2x. State
(i) the amplitude of f
(ii) the period of f
(iii) the maximum and minimum values of f
(iv) Sketch the graph of y = f(x)
Answer by ikleyn(52803) About Me  (Show Source):
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The function f is defined for 0 ≤ x ≤ 2pi, by f(x) = 3 + 5sin2x. State
(i) the amplitude of f
(2) the period of f
(3) the maximum and minimum values of f
(4) Sketch the graph of y = f(x)
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(1)  The amplitude of f(x) is 5 units, obviously: the coefficient at sin(2x).



(2)  The period of f(x) is pi, obviously: half of the period of sin(x), the base parent function.


     So, in the given interval from 0 to 2pi, you will have two periods.



(3)  The maximum of f(x) is  3 + 5 = 8.

     The minimum of f(x) is  3 - 5 = -2.


     The mid-line is  y = 3.



(4)  Make a sketch on your own.

     Or use the online plotting tool at www.desmos.com/calculator.  It is free of charge.


     All you need for it is to print the formula for the function in the input port.

Solved.