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-axisB. vertical compression by a factor of 2, vertical translation 3 units down, reflection across the x-axisC. reflection across the x-axis, vertical stretching by a factor of 2, vertical translation 3 units upD. reflection across the y-axis, vertical stretching by a factor of 2, vertical translation 3 units down
Accepted Solution
A:
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