Question

Using the graphed function above, find the following

Answer 1

See attached a picture of the graphed function and a file with the whole answer.

Answer:

• 1. Maximum: f(x) = 7.

• 2. Minimum: f(x) = - 3.

• 3. Equation of the midline: y = 2.

• 4. Amplitude: 5

• 5. Period:  4

• 6. Frequency: 1/4 = 0.25

• 7. Equation of the function:

                  $f(x)=5sin(\pi x/2)+2$

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.

• y = 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.

• amplitude = 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).

• period = 4

6. Frequency

Frequency is the inverse of the period. Hence, you just must divide 1 by period:

• $frequency=1/period=1/4=0.25$

Since the site is not letting to upload the complete answer here, I attach a file with the whole answer.