Option a. f(x) = sin (x - [tex]\pi[/tex]) - 4 is the required sine function
Step-by-step explanation:
Step 1 :
Given,
Amplitude = 1
period = 2[tex]\pi[/tex]
horizontal shift = [tex]\pi[/tex]
Vertical shift = -4
Step 2 :
The sine function's equation is as follows :
f(x) = a sin(bx + c) + d
where
a represents the amplitude
b represents the period, obtained by dividing the given period by 2 [tex]\pi[/tex]
c represents the horizontal shift
d represents the vertical shift
Step 3:
So here we have,
a = 1
b = 2 [tex]\pi[/tex] / 2[tex]\pi[/tex] = 1
c = - [tex]\pi[/tex] (assuming the wave is shifted to the right)
d= -4
Substituting the values in the sine function we get
f(x) = sin (x - [tex]\pi[/tex]) - 4
Step 4:
Answer
option a. f(x) = sin (x - [tex]\pi[/tex]) - 4 is the required sine function
