question 19 (1 point) (09.03 mc) izzys heartbeat rate was measured on an ekg machine. after conversion, the…

question 19 (1 point) (09.03 mc) izzys heartbeat rate was measured on an ekg machine. after conversion, the function produced could be modeled by a sine function, and the wave produced a maximum of 8, minimum of -2, and period of π. which of the following functions could represent izzys ekg read - out? a f(x)=8 sin πx - 2 b f(x)=5 sin πx + 3 c f(x)=5 sin 2x + 3 d f(x)=2 sin 2x + π

question 19 (1 point) (09.03 mc) izzys heartbeat rate was measured on an ekg machine. after conversion, the function produced could be modeled by a sine function, and the wave produced a maximum of 8, minimum of -2, and period of π. which of the following functions could represent izzys ekg read - out? a f(x)=8 sin πx - 2 b f(x)=5 sin πx + 3 c f(x)=5 sin 2x + 3 d f(x)=2 sin 2x + π

Answer

Explanation:

Step1: Find the amplitude

The amplitude $A$ of a sine - function $y = A\sin(Bx - C)+D$ is given by $A=\frac{\text{max}-\text{min}}{2}$. Here, $\text{max} = 8$ and $\text{min}=-2$, so $A=\frac{8 - (-2)}{2}=\frac{10}{2}=5$.

Step2: Find the vertical shift

The vertical shift $D$ is given by $D=\frac{\text{max}+\text{min}}{2}=\frac{8+( - 2)}{2}=\frac{6}{2}=3$.

Step3: Find the value of $B$

The period $T$ of a sine - function $y = A\sin(Bx - C)+D$ is $T=\frac{2\pi}{B}$. Given $T = \pi$, then $\pi=\frac{2\pi}{B}$, solving for $B$ gives $B = 2$.

Answer:

C. $f(x)=5\sin2x + 3$