Question

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

Answer 1

✔ vertical compression by a factor of 0.5

reflection across the y-axis

✔ vertical translation 3 units down

vertical stretch by a factor of 0.5

✔ reflection across the x-axis

vertical translation 3 units up

vertical translation 0.5 units down

or A.), B.), and D.)

The function rule y = –0.5cos(x) – 3 describes graph

✔ c shown.

Answer 2

The correct option is;

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

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.