Answer:
[tex]f(x)=5sin(\pi x/2)+2[/tex]
Explanation:
Since no graphed function was provided with the original question, I am providing one in the attached file that may be used to answer your question.
That graph shows that the function goes between - 3 ≤ f(x) ≤ 7, is periodic, and shows several other clue features, including the y-intercept (0, 2).
1. Maximum:
The maximum value of the function is f(x) = 7.
Since it is a periodic function (the values are repeated periodically) the maximum is reached many times. Some maxima are (1,7), (5,7) which are marked on the graph, but also (-3, 7) and (9,7) are maxima.
2. Minimum:
The minimum value of the f(x) is f(x) = - 3.
Again, the periodicity of the function yields to many minima points. Some minima are: (-1, -3), (3, -3), (7, -3), and (11, -3).
3. Equation of the midline
The mid line, also known as rest line and equilibrium line, is the horizontal line (parallel to the y-axis) just in the middle between the maxima and the minima.
Hence it is y = (7 -3)/2 = 2.
In the graph it is shown with a dotted blue line.
4. Amplitude
The amplitude is the vertical distance between the midline and one maximum or one minimum.
That is | 7 - 2| = | 2 - (-3) | = 5.
5. Period
The period is the interval of repetition of the function.
You can see the function repeats every 4 units of the x-axis.
You will see below that the period is also found dividing 2π by the coefficient of the variable x (inside the argument part of the function).
6. Frequency
Frequency is the inverse of the period. Hence, you just must divide 1 by period:
