Question

20 points

In what direction and by how many units is the graph of f(x) = −3 cos(2x − π) + 2 vertically and horizontally shifted? (1 point) Down 2, left pi over 2 Down 2, right pi over 2 Up 2, left pi over 2 Up 2, right pi over 2

Answer 1

Up 2, pi/2 to the right. Hope this helps!

Answer 2

Right π over 2 Up 2.

Explanation:

We are given a trigonometric function f(x) = −3 cos(2x − π) + 2.

We need to explain the transformations in the given function being applied.

We can see that 2 is being added to −3 cos(2x − π) in th given function.

According to rules of transformations, y=f(x)+D, shifts D units up if D is a positive number.

Therefore, for adding 2 in −3 cos(2x − π), it would shift 2 units up.

Let us see other transformation being applied there.

We can see that π is being subtracted in parenthesis from 2x.

According to rules of transformations, y=f(x-C), shifts C units right if C is a positive value.

Therefore, on subtracting π from 2x in −3 cos(2x) inside parenthesis, the function shifts π units right.

Therefore, correct option for transformations would be :

Right π over 2 Up 2.