Question

Which of the following is true for f(x) = 5cos(x) +1?
The period of the function is 10 pi.
The function has an amplitude of 2.5.
A zero of the function is (StartFraction pi Over 2 EndFraction, 0).
The range of the function is the set of real numbers Negative 4 less-than-or-equal-to y less-than-or-equal-to 6.

Answer 1

Answer:

The range of the function is the set of real numbers $-4\leq y\leq6$

Step-by-step explanation:

Since the amplitude is 5, this tells us the distance between the midline and the maximum/minimum, where the function oscillates. Here, the minimum is 1-5 = -4 and the maximum is 1+5 = 6. So, the last choice is correct

Answer 2

The true statement is the last one, the range of the function is:

-4 ≤ y ≤ 6

Which statement is true?

Here we have the function:

f(x) = 5*cos(x) + 1

We can see that the amplitude is 5, the period is 2pi (like in all cosine functions that only are evaluated on x) and the midline is 1.

With that in mind, the first two statements are false, so we discard these.

The third statement says that we have a zero at pi/2, and this is also false, because we will et:

f(pi/2) = 5*cos(pi/2) + 1 = 5*0 + 1 = 1

Finally, for the last statement, we need to look at the range of our function.

f(x) =  5*cos(x) + 1

The maximum value of the function is when cos(x) = 1, it gives:

Max = 5*1 + 1 = 6

The minimum value is when cos(x) = -1, it gives:

Min = 5*-1 + 1 = -4

Then the range is: -4 ≤ y ≤ 6

Meaning that the last statement is true.

If you want to learn more about cosine functions, you can read:

https://brainly.com/question/8120556