It is given in the question , that Simon has 160 meters of fencing to build a rectangular garden. the garden's area (in square meters) as a function of the garden's width w (in meters) is modeled by
Which represents parabola and the parabola is maximum at its vertex, that is
Therefore the width is 40 meters and the area is
The general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is .
A function is a rule that relates two variables.
The parent function is:
We know the period of the parent function is 2π and the amplitude is 1.
For an amplitude of 3, we need to multiply the parent function by 3.
So, the function with amplitude 3 will be given by:
For a period of 4π, we need to make the argument of the parent function half.
So,
A horizontal shift of negative π means, f(x) will become f(x+π)
So, .
Therefore, the general equation of a cosine function with an amplitude of 3, a period of 4 π, and a horizontal shift of negative π is .
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