Asap describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). f(x)=-5.8sin x. g(x)=sin x. a: vertical stretch by a factor of 5.8, reflection across y-axis. b: vertical stretch by a factor of 5.8,reflection across x-axis. c: horizontal stretch by a factor of 5.8, reflection across x-axis. d: horizontal stretch by a factor of 5.8 reflection across y-axis.

Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer B

Step-by-step explanation:

* Lets revise the vertical and horizontal stretch with reflection

- A vertical stretching is the stretching of the graph away from the

 x-axis

- If k > 1, the graph of y = k•f(x) is the graph of f(x) vertically stretched

 by multiplying each of its y-coordinates by k.

- If k should be negative, the vertical stretch is followed by a reflection

 across the x-axis  

- A horizontal stretching is the stretching of the graph away from

 the y-axis

- If 0 < k < 1 (a fraction), the graph of y = f(k•x) is f(x) horizontally

 stretched by dividing each of its x-coordinates by k.

- If k should be negative, the horizontal stretch or shrink is followed

 by a reflection in the y-axis

* Lets solve the problem

∵ G(x) = sin x

∵ F(x) = -5.8 sin x

∴ F(x) = -5.8 G(x)

- From the rule above

∴ G(x) is stretched vertically by scale factor -5.8

∵ The scale factor is negative

∴ The vertical stretch is followed by a reflection across the x-axis  

* The transformation is:

  Vertical stretch by a factor of 5.8 , reflection across x-axis