Write an equation for the function that is described by the given characteristics.
A sine curve with a period of π,an amplitude of 4,a right phase shift of $$\frac { \pi } { 2 }$$ ,and a vertical translation up 7 units.

A)y = 10 + 4 sin (2x + π)
B)y = 7 + 4 sin (2x - π)
C)y = 9 - 4 sin (2x + π)
D)y = 8 + 4 sin (- 2x - π)
E)y = 11 + 7 sin (2x - π)

Question

Write an equation for the function that is described by the given characteristics. ​
A sine curve with a period of π,an amplitude of 4,a right phase shift of $$\frac { \pi } { 2 }$$ ,and a vertical translation up 7 units.
​
A)y = 10 + 4 sin (2x + π)
B)y = 7 + 4 sin (2x - π)
C)​y = 9 - 4 sin (2x + π)
D)y = 8 + 4 sin (- 2x - π)
E)y = 11 + 7 sin (2x - π)

Quizplus · Accepted Answer

The general form of a sine function is $y = A \sin(B(x - C)) + D$, where $A$ is the amplitude, $B$ affects the period (with the period being $2\pi / B$), $C$ is the phase shift, and $D$ is the vertical translation. For a sine curve with a period of $\pi$, amplitude of 4, a right phase shift of $\frac{\pi}{2}$, and a vertical translation up 7 units, the equation is $y = 7 + 4 \sin(2(x - \frac{\pi}{2}))$. Simplifying the phase shift part gives $y = 7 + 4 \sin(2x - \pi)$, which matches option B.

Write an Equation for the Function That Is Described by the Given