Earlier in this course, you explored Euclidean geometry, which is the study of flat space. This approach follows the teachings of Euclid, in which he describes the
relationships between points, lines, and planes without any numerical measurement.
You saw evidence of Euclidean geometry inside several proofs and geometric
constructions
In contrast, the focus of this unit is understanding geometry using positions of points
in a Cartesian coordinate system. The study of the relationship between algebra and
geometry was pioneered by the French mathematician and philosopher René
Descartes. In fact, the Cartesian coordinate system is named after him. The study of
geometry that uses coordinates in this manner is called analytical geometry.
It's clear that this course teaches a combination of analytical and Euclidean
geometry. Based on your experiences so far, which approach to geometry do you
prefer? Why? Which approach is easier to extend beyond two dimensions? What are
some situations in which one approach to geometry would prove more beneficial than
the other? Describe the situation and why you think analytical or Euclidean geometry
is more applicable.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

hi there!

the answer will be d: 2

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day