select all the correct locations on the graph.\nthe graph of a cosine function is shown. which two points on…

select all the correct locations on the graph.\nthe graph of a cosine function is shown. which two points on the mid - line of the function are separated by a distance of one period?

select all the correct locations on the graph.\nthe graph of a cosine function is shown. which two points on the mid - line of the function are separated by a distance of one period?

Answer

Answer:

We need to first identify the mid - line of the cosine function. The mid - line of a cosine function (y = A\cos(Bx - C)+D) is (y = D). From the graph, the mid - line is (y = 1.5).

The period of a cosine function (y=\cos(x)) is (2\pi). For a general cosine function (y = A\cos(Bx - C)+D), the period (T=\frac{2\pi}{B}).

We look for two points on the mid - line (y = 1.5) such that the horizontal distance between them is equal to the period of the function.

Let's assume the function is of the form (y = A\cos(Bx)+D). By observing the graph, we can see that if we start from the point on the mid - line at (x=\frac{\pi}{4}) and move to the point on the mid - line at (x=\frac{5\pi}{4}), the horizontal distance between them is (\frac{5\pi}{4}-\frac{\pi}{4}=\pi).

If we assume the function has a period of (\pi) (by observing the graph's repeating pattern), two points on the mid - line separated by one period are the points on the mid - line (y = 1.5) at (x=\frac{\pi}{4}) and (x=\frac{5\pi}{4}) (assuming the graph continues in the same pattern).

However, since we don't have the full function formula and are working with the graph, we note that for a cosine - like function, we can find the period by looking at the distance between two consecutive equivalent points (like two consecutive mid - line crossings in the same phase).

If we assume the period is (T), and we start from the mid - line crossing at (x = \frac{\pi}{4}) and find the next mid - line crossing in the same phase at (x=\frac{5\pi}{4}), these two points on the mid - line ((y = 1.5)) are separated by one period.

Explanation:

Step1: Identify mid - line

The mid - line of the function is (y = 1.5) by observing the graph.

Step2: Observe period

By looking at the repeating pattern of the graph, we find two mid - line points.

Step3: Calculate distance

The distance between the mid - line points at (x=\frac{\pi}{4}) and (x = \frac{5\pi}{4}) is (\frac{5\pi}{4}-\frac{\pi}{4}=\pi) which represents one period of the function.