which set of transformations is needed to graph (f(x)= - 0.1cos(x)-4) from the parent cosine…

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

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

Answer

Explanation:

Step1: Analyze the coefficient of cosine

The coefficient of $\cos(x)$ is $- 0.1$. The negative sign indicates a reflection across the $x$-axis, and the absolute - value $|0.1|$ represents a vertical compression by a factor of $0.1$.

Step2: Analyze the constant term

The constant term is $-4$. In the form $y = A\cos(x)+k$, the value of $k=-4$ indicates a vertical translation of 4 units down.

Answer:

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