Question

What sine function represents an amplitude of 4, a period of pi over 2, no horizontal shift, and a vertical shift of −3?

Answer 1

Answer:

$f(x) = 4sin(\frac{\pi}{2}x) - 3$, the third one

Step-by-step explanation:

Explaining the sine function:

The sine function is defined by:

$S = Asin(p(x - x_{0})) + V$

In which A is the amplitude, $p = \frac{2\pi}{N}$ is the period, $x_{0}$ is the horizontal shift and V is the vertical shift.

So, in your problem:

The amplitude is 4, so A = 4.

The period is $\frac{\pi}{2}$, so $p = \frac{\pi}{2}$.

There is no horizontal shift, so $x_{0} = 0$.

The vertical shift is −3, so V = -3.

The sine function that represents these following conditions is

$f(x) = 4sin(\frac{\pi}{2}x) - 3$, the third one