:3 what is the average rate of change of the function f(x)=4(2)x from x = 0 to x = 2?

Please, Abby, use " ^ " to denote exponentiation: f(x) = 4(2)^x.

The rate of change of this function, on [0,2], is

4(2)^2 - 4(2^0) 16 - 4

= = 6 units per unit change in x

2 - 0 2

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'.