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Identify the transformations needed to graph the cosine function y = –0.5cos(x) – 3 from the parent cosine function. Check all that apply.

vertical compression by a factor of 0.5

reflection across the y-axis

vertical translation 3 units down

vertical stretch by a factor of 0.5

reflection across the x-axis

vertical translation 3 units up

vertical translation 0.5 units down

Respuesta :

tahamohammed01
vertical translation 3 units down, vertical compression by a factor of 0.5, and reflection across the x-axis. This is because since the number -3 is outside of the parenthesis, it is a vertical translation and is since it is negative it is 3 down. If the number multiplied by the function is less than 1 it is a compression and if it is greater than 1 it is a stretch. And the negative represents the reflection across the x axis.

Using translation concepts, it is found that the transformations that apply are:

  • vertical compression by a factor of 0.5.
  • reflection across the x-axis.
  • vertical translation 3 units down.

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 cosine function is given by:

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

First, the function was multiplied by -0.5, which means that:

  • Since 0.5 < 1, the function was vertically compressed.
  • Since it was multiplied by a negative number, it was reflected across the x-axis.

Then, 3 was subtracted from the function, which means that it was shifted 3 units down.

You can learn more about translation concepts at https://brainly.com/question/4521517

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