Plz im struggling in this lesson : ( what graph represents the piecewise-defined function?

y=⎧⎩⎨⎪⎪6   if  x≤−33   if  −3

Well im not good at this ,butt I'll tell you something. An open dot means that point is not included , soo something like y<208 would mean 208 is not included and have an open dot, butt a closed dot means the point is included, such as <_ 450. ( The line is supposed to be under < butt i don't know how to do that.)  Hope this helps

The piecewise function is not clear, so I will represent every function in the plots.

The Top left option:

y = 3 if x ≤ 1

y = x if x > 1

Top right option:

y = 3 if x < 1

y = 1 if x ≥ 1

Bottom left option:

y = 3 if x ≤ 1

y = 1 if x > 1

Bottom right option:

y = 3 if x < 1

y = x if x ≥ 1

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'.

answer: x=3 and y=4

step-by-step explanation: