Beth and Jenny are meeting at Beth's grandmother's house next week to help her clean out her attic. The girls draw a map to plan out their route. Beth lives 3 miles from her grandmother and Jenny lives 4 miles from Beth's grandmother. The girls use the map to figure out how far they live from each other. On a separate sheet of paper, draw a coordinate plane. Label the x and y axis, as well as the origin. Randomly choose a point to represent Beth's grandmother's house. Make sure to label the point. From the point, map out a straight line distance to Beth's house. Label the point as Beth's house. Return to Grandmother's house and count a straight line distance to Jenny's house. Make sure to travel in a different direction from Beth's house. Label the point as Jenny's house. Using the distance formula, find the straight line distance between Beth and Jenny's houses. Complete your work in the space provided or upload a file that can display math symbols if your work requires it. Include the coordinate plane with all points and axes labeled, the distance between Beth and Jenny's house and the steps that you took to find the distance between the houses.

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.

idk

step-by-step explanation:

i don't know

see below

step-by-step explanation:

x+2> 6

subtract 2 from each side

x+2-2 > 6-2

x > 4

there is an open circle at 4 since is it is greater than and the line goes to the right

vertical asymptote .

horizontal asymptote .

step-by-step explanation:

given function is .

vertical asymptote is given by setting

denominator =0

when degree of numerator and denominator are same then divide first term of numerator by first term of denominator to get horizontal asymptote.