Answer:
Option: A is the correct answer.
A. [tex]y=4\sin(x+1)-2[/tex]
Step-by-step explanation:
By looking at the graph we observe that the maximum value of the function is 2 and the minimum value pf the function is: -6
Also the maximum value is obtained at
B)
[tex]y=4\cos(x-1)+2[/tex]
The maximum/minimum value of the function is obtained when the cosine function is maximum/minimum.
As we know that maximum value of cosine function is: 1
and minimum value of cosine function is: -1
Hence, we get maximum value of the given function is: 6
and minimum value of the given function is: -2
Hence, option: B is incorrect.
C)
[tex]y=6 \sin(x+1)-2[/tex]
The maximum/minimum value of the function is obtained when the sine function is maximum/minimum.
As we know that maximum value of sine function is: 1
and minimum value of sine function is: -1
Hence, we get maximum value of the given function is: 6-2=4
and minimum value of the given function is: -6-2= -8
Hence, option: C is incorrect.
D)
[tex]y=4\sin(x-1)-2[/tex]
The maximum/minimum value of the function is obtained when the sine function is maximum/minimum.
As we know that maximum value of sine function is: 1
and minimum value of sine function is: -1
Hence, we get maximum value of the given function is: 4-2=2
and minimum value of the given function is: -4-2= -6
Also, when x=1 we have:
y= -2
but at x=1 the value of the function is positive.
Hence, option: D is incorrect.
A)
[tex]y=4\sin(x+1)-2[/tex]
When we graph the function we see that it matches the given graph and hence, option: A is correct.
