which of the following is true for (f(x)=5cos(x)+1)?\nthe period of the function is (10pi).\nthe function…

Explanation:

Step1: Recall period formula for cosine

For $y = A\cos(Bx)+C$, period $T=\frac{2\pi}{|B|}$. Here $B = 1$, so $T = 2\pi\neq10\pi$.

Step2: Recall amplitude formula for cosine

Amplitude of $y=A\cos(Bx)+C$ is $|A|$. Here $A = 5$, amplitude is $5\neq2.5$.

Step3: Check for zero - point

Set $f(x)=0$, so $5\cos(x)+1 = 0$, then $\cos(x)=-\frac{1}{5}$. When $x = \frac{\pi}{2}$, $\cos(\frac{\pi}{2})=0$, so $(\frac{\pi}{2},0)$ is not a zero.

Step4: Find the range

The range of $\cos(x)$ is $[- 1,1]$. For $y = 5\cos(x)+1$, when $\cos(x)=-1$, $y=5\times(-1)+1=-4$; when $\cos(x)=1$, $y=5\times1 + 1=6$. So the range is $-4\leq y\leq6$.

Answer:

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