Q:

HELP ASAP PLEASE!!!!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.

Accepted Solution

A:
Answer:Vertical stretch by a factor of 5.8 , reflection across x-axis ⇒ answer BStep-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