The black graph is the graph of y = f(x) . Choose the equation for the red graph

B

Step-by-step explanation:

I would say make a quick table for each:

black:

Y     I    X

-2         4

-1         -2, 3.5

0         -.75, 3

1           .75, 2.5

2         2

Red:

Y     I    X

-2         2

-1         -1, 1.75

0         -.25, 1.5

1           .25, 1.25

2         1

The x's are almost half in the red as in the black graph.

Thinking logically you can see that the Y points stay the same so you can rule out C and D, and since the graph got smaller not bigger dividing by two will give the graph not multiplying.

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.