The exponential function, f(x) = 2^x, undergoes two transformations to g(x) = 1/3 x 2^x - 7. how does the graph change? select all that apply. a. it is vertically compressed. b. it is vertically stretched. c. it is shifted right. d. it is shifted down e. it is lipped over the x-axis.

options A and D are the correct options.

Step-by-step explanation:

The parent exponential function is f(x) = 2ˣ

Now this function undergoes two transformations to form g(x) =

When parent function f(x) = 2ˣ  is multiplied by , this means f(x) has been compressed vertically because < 1.

Now we subtract 7 from the new function , that means we are shifting this function 7 units downwards on y-axis.

Therefore, options A and D are the correct options.

a) justify

step-by-step explanation:

justifying is just part of everyday life. justify kind of means proof so i think the answer is a) justify.

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'.