Question

HELP PLZ ASAP!

Which set of transformations is needed to graph f(x) = –2sin(x) + 3 from the parent sine function?
A. vertical compression by a factor of 2, vertical translation 3 units up, reflection across the y-axis
B. vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axis
C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up
D. reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down

Answer 1

reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up

Explanation:

Answer 2

The main function is given by:
f (x) = sine (x)
We then have the following transformations:

Reflections:
Reflection or turning is the mirror image of a figure. It can also be said that it is the turning of points and graphs around the axes.
To graph y = -f (x), reflect the graph of y = f (x) on the x-axis. (Vertical reflection)
f (x) = - sine (x)

Expansions and vertical compressions:
To graph y = a*f (x)
If a> 1, the graph of y = f (x) is expanded vertically by a factor a.
f (x) = - 2 * sine (x)

Vertical translations
Suppose that k> 0
To graph y = f (x) + k, move the graph of k units up.
f (x) = - 2 * sine (x) + 3

Answer:
C. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units up