Answer:
[tex]y=sinx +2[/tex]
Step-by-step explanation:
We have to choose the function whose graph is given.
A.[tex]y=sinx+2[/tex]
Substitute x=0 then
[tex]y=0+2=2[/tex]
Therefore, y- intercept is at y=2.
Substitute [tex]x=\frac{\pi}{2}[/tex]
[tex]y=sin\frac{\pi}{2}+2=1+2=3[/tex] because ([tex]\sin\frac{\pi}{2}=1[/tex])
Substitute [tex]x=-\frac{\pi}{2}[/tex]
Then we get
[tex]y=sin(-\frac{\pi}{2})+2=-sin\frac{\pi}{2}+2=-1+2=1[/tex]
[tex] sin (-x)=-sinx[/tex]
Therefore, given graph is [tex]y=sinx +2[/tex]
B.[tex]y=-sinx+2[/tex]
When Substitute [tex]x=-\frac{pi}{2}[/tex]
Then, [tex]y=-sin(-\frac{\pi}{2})+2=sin\frac{pi}{2}+2=1+2=3[/tex]
But in graph at [tex]x=-\frac{pi}{2}[/tex] , y=-1
So,It is not true.
C.[tex]y=cosx+2[/tex]
When x=0
then we get [tex]y=cos0+2=1+2=3[/tex] (cos 0=1)
But in graph y - intercept at y=2
So, it is false.
D.[tex]y=-cosx+2[/tex]
Substitute x=0
Then, we get
[tex]y=-cos 0+2=-1+2=1[/tex]
So, it is false.
Answer: [tex]y=sinx +2[/tex]
