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.

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Ashraf82 Ashraf82 · Answer 1 · 2019-06-21T15:43:31+02:00

Answer:

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