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the graph of y = cos(x) was shifted downwards by 3 units, shrink horizontally by a fourth of a unit, inverted horizontally and shifted 60° to the left. if it has an amplitude of 5 units, write the equation of the resulting graph.​

Respuesta :

Using translation concepts, it is found that the equation of the resulting graph is given by:

[tex]y = 2.5(\cos{(4x - 60^\circ)} - 3)[/tex]

What is a translation?

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

The parent function is given by:

[tex]y = \cos{x}[/tex]

The transformations are as follows:

  • Shift down of 3 units, hence [tex]y = \cos{x} - 3[/tex].
  • Shrink horizontally by a fourth of a unit, hence [tex]y = \cos{(4x)} - 3[/tex].
  • Inverted horizontally, hence [tex]y = \cos{-4x} - 3 = \cos{(4x)} - 3[/tex], as the cosine function is even.
  • Shifted 60° to the left, hence [tex]y = \cos{(4x - 60^\circ)} - 3[/tex]
  • Amplitude of 5 units, hence the function is multiplied by 5/2 = 2.5, that is, [tex]y = 2.5(\cos{(4x - 60^\circ)} - 3)[/tex].

More can be learned about translation concepts at https://brainly.com/question/4521517

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