Which of the following functions has a maximum y value of 4?y = cos x + 4y = cos( x + 4)y = 4cos xy = cos4 x

To find the function that has a maximum y value of 4, we need to analyze each of the given options step by step.

1. y = cos x + 4: This function has a constant term of 4 added to the cosine function. The cosine function oscillates between -1 and 1, so adding 4 to it will shift the entire graph upwards by 4 units. However, the maximum value of the cosine function itself is 1, so the maximum value of this function would be 1 + 4 = 5, not 4. Therefore, this function does not have a maximum y value of 4.

2. y = cos(x + 4): This function is similar to the first one, but the cosine function is now shifted horizontally by 4 units to the left. Again, the maximum value of the cosine function is 1, so adding 4 to it will not result in a maximum y value of 4. Therefore, this function also does not have a maximum y value of 4.

3. y = 4cos x: In this function, the cosine function is multiplied by a constant factor of 4. This means that the amplitude of the cosine function is increased to 4. The maximum value of the cosine function is still 1, so multiplying it by 4 will result in a maximum y value of 4. Therefore, this function has a maximum y value of 4.

4. y = cos4 x: This function has the cosine function raised to the power of 4. The maximum value of the cosine function is 1, and raising it to the power of 4 will still result in a maximum value of 1. Therefore, this function does not have a maximum y value of 4.

In conclusion, the function that has a maximum y value of 4 is y = 4cos x.