Question

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

Answer 1

Answer:

D

Step-by-step explanation:

Answer 2

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:

A.

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 $10\pi$.

B.

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.

C.

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.

D.

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.

ANSWER: Last choice, choice D.