Which functions has the graph shown?

C.

Step-by-step explanation:

Let's identify some points here that are on the graph:

(0,0), (pi/2,-1), (pi,0).

Let's see if this is enough.

We want to see which equation holds for these points.

Let's try A.

(0,0)?

y=cos(x-pi/2)

0=cos(0-pi/2)

0=cos(-pi/2)

0=0 is true so (0,0) is on A.

(pi/2,-1)?

y=cos(x-pi/2)

-1=cos(pi/2-pi/2)

-1=cos(0)

-1=1 is false so (pi/2,-1) is not on A.

The answer is not A.

Let's try B.

(0,0)?

y=cos(x)

0=cos(0)

0=1 is false so (0,0) is not on B.

The answer is not B.

Let's try C.

(0,0)?

y=sin(-x)

0=sin(-0)

0=sin(0)

0=0 is true so (0,0) is on C.

(pi/2,-1)?

y=sin(-x)

-1=sin(-pi/2)

-1=-1 is true so (pi/2,-1) is on C.

(pi,0)?

y=sin(-x)

0=sin(-pi)

0=0 is true so (pi,0) is on C.

So far C is winning!

Let's try D.

(0,0)?

y=-cos(x)

0=-cos(0)

0=-(1)

0=-1 is not true so (0,0) is not on D.

So D is wrong.

Okay if you do look at the curve it does appear to be a reflection of the sine function.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.