A sinusoidal function whose frequency is 3, maximum value is 12, minimum value is −6 , and y-intercept is (0, 3) .

Which function could be the function described?



f(x)=9sin(6πx)+3

f(x)=9sin(x3)−3

f(x)=9sin(3x)+3

f(x)=9sin(6πx)−6 <my answer

almost. If the max is 12 and the min is -6 then the midpoint is at (12-6)/2 = 3

So, f(x)=9sin(6πx)+3

your choice has
max = -6+9 = 3
min = -6-9 = -15

To determine the correct function, we need to analyze the given information about the sinusoidal function. Let's go through each option and find the one that matches the given criteria:

Option 1: f(x) = 9sin(6πx) + 3
Looking at the frequency, 6πx, we can see that it is twice the desired frequency of 3. Therefore, this option does not match the given frequency.

Option 2: f(x) = 9sin(x3) - 3
The frequency in this option is x3, which is not the desired value of 3. Therefore, this option does not match the given frequency.

Option 3: f(x) = 9sin(3x) + 3
In this option, the frequency is 3x, matching the desired frequency of 3. Additionally, the maximum value is 9 (amplitude of 9 multiplied by the sine function's maximum value of 1), and the minimum value is -6 (amplitude of 9 multiplied by the sine function's minimum value of -2/3). Thus, this option matches all the given criteria.

Option 4: f(x) = 9sin(6πx) - 6
Similar to option 1, the frequency is given as 6πx, which does not match the desired frequency of 3. Therefore, this option does not match the given frequency.

Therefore, the correct function that matches the description is f(x) = 9sin(3x) + 3.

To determine the correct function, we can look at the given information:

1. Frequency is 3: This indicates that the period of the function is 3.

2. Maximum value is 12: This means that the amplitude of the function is (12 - 3)/2 = 9/2 = 4.5.

3. Minimum value is -6: Therefore, the average value of the function is (-6 + 3)/2 = -1.5.

4. Y-intercept is (0, 3): This tells us that the value of the function at x = 0 is 3.

Comparing these characteristics with the given options:

a) f(x) = 9sin(6πx) + 3: This function has the correct amplitude, frequency, and y-intercept, but it does not have the correct average value.

b) f(x) = 9sin(x/3) - 3: This function has the correct amplitude, average value, and y-intercept, but it does not have the correct frequency.

c) f(x) = 9sin(3x) + 3: This function has the correct amplitude, frequency, and y-intercept, and it also has the correct average value (-6 + 3)/2 = -1.5.

d) f(x) = 9sin(6πx) - 6: This function has the correct amplitude, frequency, and y-intercept, but it does not have the correct average value.

Therefore, the correct function is f(x) = 9sin(3x) + 3.