Which of the following is true for f(x) = 5cos(x) +1?

a.) the period of the function is 10 pi
b.) the function has an amplitude of 2.5.
c.) a zero of the function is ( pi/2, 0 )
the range of the function is the set of real numbers -4≤ y ≤ 6

The function is the cosine curve with 5 as the amplitude and is shifted 1 units up.

Let's check all the 4 choices:

A.

The period of a function in the form (which is the function in this problem) has period . Period would have changed if there was any coefficient of x in the argument. But it doesn't so period is NOT .

B.

The amplitude of a function in the form (which is the function in this problem) is A. But A is 5 here so the amplitude is definitely NOT 2.5.

C.

A zero of the function is given as , which means that if we plug in into x, it should give us 0. Let's check:

. It's not true.

D.

We know that this function has an amplitude of 5, so the part ranges from -5 to 5. But this part is shifted 1 units up, so the max amplitude is and the min is . So we can say that the range of the function is the set of real numbers from -4 to 6. This choice is correct.

ANSWER: Last choice, choice D.

probably the last option

step-by-step explanation: