Question

A cosine function has a period of 5, a maximum value of 20, and a minimum value of 0. The function is not a reflection of its parent function over the x-axis.

Which function could be the function described?

A: f(x)=10cos(2π/5 x)+10
B: f(x)=10cos(5x)−10
C: f(x)=−10cos(5x)+10
D: f(x)=−10cos(2π/5 x)+10

Answer 1

`f(x)=10cos((2\pi )/(5) x) + 10`

Explanation:

Answer 2

A: f(x)=10cos(2π/5 x)+10

Explanation:

The coefficient of x in the cosine argument of the function will be 2π/period. Since the period is 5, the coefficient is 2π/5. This observation eliminates choices B and C.

The description "not a reflection of the parent function over the x-axis" means the multiplier of the cosine function is not negative, eliminating choice D.

The remaining choice A matches the description.