Which graph represents the function g(x) = |x +4|+ 2?

Step-by-step explanation: The graph on the left.

When graphing absolute functions, whatever is inside the absolute value signs corresponds to the distance you move horizontally, but you must move in the opposite direction of the sign in front  of the number. In this case you would move four units to the left. The vertical shift corresponds to the number outside of the absolute value signs, in this question you move two units. The direction you move is the same as the sign in front of the number, which means you would move up two units.

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'.

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb