Mathematics: 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

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

Ответ:

maystrenko53

10.01.2022

The function f(x)=5cos(x)+1 is the cosine curve with 5 as the amplitude and is shifted 1 units up.

Let's check all the 4 choices:

The period of a function in the form f(x)=Acos(x)+B (which is the function in this problem) has period $2\pi$ . Period would have changed if there was any coefficient of x in the argument. But it doesn't so period is NOT $10\pi$ .

The amplitude of a function in the form f(x)=Acos(x)+B (which is the function in this problem) is A. But A is 5 here so the amplitude is definitely NOT 2.5.

A zero of the function is given as $(\frac{\pi}{2},0)$ , which means that if we plug in $\frac{\pi}{2}$ into x, it should give us 0. Let's check:

$5cos(\frac{\pi}{2})+1\\=5(0)+1\\=1$ . It's not true.

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