Question

In: Advanced Math

For the following exercises, determine the amplitude, period, and midline of the graph, and then find a formula for the function.

Give in terms of a sine function.

Expert Solution

Consider the graph provided in the exercise:

For a sinusoidal function, the Amplitude |A| is as follows:

|A| = 1/2|maximum-minimum|

Since the maximum point is -2 and minimum point is -6

Therefore the amplitude is:

|A| = 1/2|2 – (-2)|

= 1/2|2 + 2|

= 1/2|4|

= 2

Period of a function is interval in which the graph of a function repeats itself.

Since the graph of sine function repeats after every 2 units, therefore the period is 2.

Midline is the equation of the point which is equidistant from the maximum and the minimum point.

y = 0

Since the graph is formed by stretching the sine graph by 2 times and shifting the sine graph to right by 1 unit.

Therefore, the formula for the given graph is as follows:

y = 2sin{π(x – 1)}.

Therefore, the formula for the given graph is as follows:

y = 2sin{π(x – 1)}.

Junaid answered 1 year ago

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