Which set of transformations is needed to graph f(x) = -0.1cos(x) - 4 from the parent cosine function? reflection across the y-axis, vertical compression by a factor of 0.1, vertical translation 4 units up

reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

vertical stretching by a factor of 0.1, vertical translation 4 units down, reflection across the y-axis

vertical stretching by a factor of 0.1, vertical translation 4 units up, reflection across the x-axis

The correct option is;

Reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down

Step-by-step explanation:

The given function is f(x) = -0.1·cos(x) - 4

The parent cosine function is cos(x)

Therefore, f(x) = -0.1·cos(x) - 4 can be obtained from the parent cosine function as follows;

The negative sign in the function gives a reflection across the x-axis

The 0.1 factor of the cosine function gives a compression of 0.1

The constant -4, gives a vertical translation 4 units down

Therefore, the correct option is a reflection across the x-axis, vertical compression by a factor of 0.1, vertical translation 4 units down.

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula