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Select all the correct answers.
Consider functions f and g.
f(x) = - 2 cos (x - 1) + 3
g(x) = 2 cos (x + 3) - 3
Which statements describe transformations of the graph of fresulting in the graph of function g?
A. The graph of function f has been vertically stretched by a factor of 4.
B. The graph of function fhas been reflected over the y-axis.
C. The graph of function fhas been reflected over the x-axis.
D. The graph of function fhas been translated 3 units down.
D. The graph of function fhas been translated 4 units left.
E. The graph of function fhas been translated 3 units left.

((More than one))

Respuesta :

xero099

The function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

How to determine the characteristics of rigid transformations by comparing two functions

In this problem we have two functions related to each other because of the existence of rigid transformations. Rigid transformations are transformations applied to geometric loci such that Euclidean distance is conserved at every point of the geometric locus.

Let be f(x) = - 2 · cos (x - 1) + 3, then we use the concept of horizontal translation 4 units in the + x direction:

f'(x) = - 2 · cos (x - 1 + 4) + 3

f'(x) = - 2 · cos (x + 3) + 3     (1)

Now we apply a reflection over the x-axis:

g(x) = - [- 2 · cos (x + 3) + 3]

g(x) = 2 · cos (x + 3) - 3

Therefore, the function g(x) is created by applying an horizontal translation 4 units left and a reflection over the x-axis. (Correct choices: Third option, fifth option)

To learn more on rigid transformations: https://brainly.com/question/1761538

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