The table shows the relationship between the average number of hours students studied for a mathematics test and their average grade.
Hours
Studied
Average
Grade
0
62
1
78
2
85
5
74
Which type of function is most likely to model these data?
A
linear function with positive rate of change
O
B
linear function with negative rate of change.
non-linear function that decreases then increases
D
non-linear function that increases then decreases

D

Step-by-step explanation:

I'm going to ponder a guess that the numbers shown, 0, 62, 1, 78, 2 ,etc. are part of a table. Having said that, the answers, when graphed, create a sort of parabola, meaning that the function itself is non-linear. This exterminates option A and B. Now its just a matter of seeing which way it goes, and since 78 is higher than 62, and 85 is higher than 78, it obviously increases, rather than decreases. This makes D our final answer.

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'.