A cosine function has a period of 3, a maximum value of 20, and a minimum value of 0. The function is a reflection of its parent function over the x-axis.

Which function could be the function described?

f(x)=10cos(3x)−10

f(x)=10cos(2π3x)+10 <my choice

f(x)=−10cos(2π3x)+10

f(x)=−10cos(3x)+10

where did you learn to write fractions? 2π/3 is the way to write it.

However, your choice is not quite correct. You forgot the reflection part. So, the correct answer is

f(x) = −10cos(2π/3 x)+10

-10cos(2π/3 x) has max/min at 10,-10 and is a reflection of cos(2π/3 x)

Now add 10 and you get max/min at 20,0

Well, let's take a look at your options. Option A: f(x)=10cos(3x)−10. That doesn't seem right because it has a minimum value of -10 instead of 0. Option B: f(x)=10cos(2π/3x)+10. Ah, that's the ticket! It has the correct period of 3, a maximum value of 20, and a minimum value of 0. Keep in mind, though, this function is a reflection over the x-axis, so it's like looking in a mathematically mirrored funhouse mirror!

To determine the correct function, we can analyze the given information:

- The period of the cosine function is the distance it takes for the function to repeat itself. In this case, the period is given as 3.
- The maximum value of the cosine function is 20, which means that the cosine function reaches a peak of 20 at some point.
- The minimum value of the cosine function is 0, which means that the cosine function reaches a minimum of 0 at some point.
- The function is described as a reflection over the x-axis, which means that the graph of the function is reflected downwards.

Based on this information, the correct function would be:
f(x) = -10cos(2π/3x) + 10

This function has a period of 3, reflects the parent function over the x-axis, and has a maximum value of 20 and a minimum value of 0. Thus, the correct choice is:
f(x) = -10cos(2π/3x) + 10

To determine which function could be the function described, we can analyze the given characteristics of the cosine function.

1. The period of the cosine function is 3. The period of a cosine function is given by 2π/b, where b represents the coefficient of x. In this case, we have 2π/3 as the period.

2. The maximum value of the cosine function is 20. The maximum value of the cosine function with a general form of f(x) = a*cos(bx) + c is given by |a| + c. In this case, it is |10| + (-10) = 10 - 10 = 0.

3. The minimum value of the cosine function is 0. The minimum value of the cosine function with a general form of f(x) = a*cos(bx) + c is given by -|a| + c. In this case, it is -|10| + (-10) = -10 - 10 = -20.

Based on these characteristics, we can eliminate options (f(x) =10cos(3x)−10) and (f(x) =−10cos(3x)+10) as they do not satisfy the given maximum and minimum values.

Now, let's analyze the remaining options:

Option 1: f(x) = 10cos(2π/3x)+10
- The period is 2π/((2π/3)x) = 3, which satisfies the given condition.
- The maximum value is |10| + 10 = 20, which also satisfies the given condition.
- The minimum value is -|10| + 10 = 0, which satisfies the given condition.
- In addition, this option is a reflection over the x-axis, as indicated in the problem statement.

Therefore, the correct choice for the function described is f(x) = 10cos(2π/3x)+10.