Answer:
[tex]f(x) = 4sin(\frac{\pi}{2}x) - 3[/tex], the third one
Step-by-step explanation:
Explaining the sine function:
The sine function is defined by:
[tex]S = Asin(p(x - x_{0})) + V[/tex]
In which A is the amplitude, [tex]p = \frac{2\pi}{N}[/tex] is the period, [tex]x_{0}[/tex] is the horizontal shift and V is the vertical shift.
So, in your problem:
The amplitude is 4, so A = 4.
The period is [tex]\frac{\pi}{2}[/tex], so [tex]p = \frac{\pi}{2}[/tex].
There is no horizontal shift, so [tex]x_{0} = 0[/tex].
The vertical shift is −3, so V = -3.
The sine function that represents these following conditions is
[tex]f(x) = 4sin(\frac{\pi}{2}x) - 3[/tex], the third one
