Miles has a square garden in his backyard. He decides to decrease the size of the garden by 1 foot on each side in order to make
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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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The function sits with its starting point at the origin. The function
is translated h units to the left or right and k units up or down. Since our radicand, the value under the square root sign, is x+7, putting that into our standard form it would be x-(-7) because minus a negative is a positive. So we move the parent graph to the left (-7 moves to the left) 7 units. There is no number k so our function is not moving up or down. Only to the left 7.