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The parent cosine function is transformed to create function
d.
d(x)= cos(2x-1) +5
To create function d, the graph of the parent cosine function undergoes these transformations:

horizontal shift A. right 0.5 of a unit B. left 1 unit C. right 1 unit D. left 0.5 of a unit

vertical shift: A. down 5 units B. up 5 units C. down 1 unit D. up 1 unit

frequency: A. remains the same B. increases by a factor of 2 C. decreases by a factor of 1/2

Respuesta :

Using translation concepts, it is found that the transformations to create function d are given as follows:

  • Horizontal shift right 1 unit.
  • Vertical shift up 5 units.
  • Frequency multiplied by 2.

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.

In this problem, the parent cosine function is given by:

f(x) = cos(x).

The translated function is given by:

d(x) = cos(2x - 1) + 5.

Which means that:

  • 1 was subtracted in the domain, hence the was a horizontal shift right 1 unit.
  • 5 was added in the range, hence there was a vertical shift up 5 units.
  • There was a multiplication by 2 in the domain, hence the frequency is multiplied by 2.

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

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