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

answer-

solution-

the given function,

the parent cosine function is,

1. for

as there is a negative sign in the cos x, so all the points with coordinate (x, cos x) becomes (x, -cos x)

∴ it is reflected over x-axis.

2. for

as a scale factor of 0.1 (i.e < 1) is multiplied, so it is compressed by a factor of 0.1

3. for

as 4 is subtracted from the f(x), so all point with coordinate (x, f(x)) becomes (x, f(x)-4)

∴ it is translated 4 units down.

therefore, a series of processes

yield the given function from its parent function.

x= cost per bracelet

number of bracelets * x + shipping charge = total cost

so

9x+9=72