which of the following is true for (f(x)= - 2sin(x)-3)?\nthe range of the function is the set of real…

Answer:

The amplitude of the function is 2.

Explanation:

Step1: Recall range formula for $y = A\sin(x)+B$

The range of $y = A\sin(x)+B$ is $[B - |A|,B + |A|]$. For $y=-2\sin(x)-3$, $A=-2$ and $B = - 3$. So range is $[-3-2,-3 + 2]=[-5,-1]$, not $-2\leq y\leq2$.

Step2: Analyze vertical - shift

The graph of $y=-2\sin(x)-3$ is the graph of $y = - 2\sin(x)$ shifted 3 units down, not up.

Step3: Recall amplitude formula

The amplitude of $y = A\sin(x)+B$ is $|A|$. For $y=-2\sin(x)-3$, $A=-2$, so amplitude $|A| = 2$.

Step4: Recall period formula

The period of $y = A\sin(Bx)+C$ is $T=\frac{2\pi}{|B|}$. For $y=-2\sin(x)-3$, $B = 1$, so period $T = 2\pi$, not $4\pi$.