The two dot plots below compare the forearm lengths of two groups of schoolchildren: two dot plots are shown one below the other. the title for the top dot plot is forearm length, group x and the title for the bottom plot is forearm length, group y. below the line for each dot plot is written length in inches. there are markings from 10 to 13 on each line at intervals of one. for the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. for the bottom line there are 2 dots above the second mark, 2 dots above the third mark, and 6 dots above the fourth mark. based on the visual inspection of the dot plots, which group appears to have the longer average forearm length? group x, because no child in the group has a forearm length longer than 12 inches. group x, because four children in the group have the least forearm length of 10 inches. group y, because a child in the group has the least forearm length of 10 inches. group y, because six children have a forearm length longer than 12 inches.

After a dreary day of rain, the sun peeks through the clouds and a rainbow forms. you notice the rainbow is the shape of a parabola. the equation for this parabola is y = -x2 + 36. graph of a parabola opening down at the vertex 0 comma 36 crossing the x–axis at negative 6 comma 0 and 6 comma 0. in the distance, an airplane is taking off. as it ascends during take-off, it makes a slanted line that cuts through the rainbow at two points. create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow. analyze the two functions. answer the following reflection questions in complete sentences. what is the domain and range of the rainbow? explain what the domain and range represent. do all of the values make sense in this situation? why or why not? what are the x- and y-intercepts of the rainbow? explain what each intercept represents. is the linear function you created with your table positive or negative? explain. what are the solutions or solution to the system of equations created? explain what it or they represent. create your own piecewise function with at least two functions. explain, using complete sentences, the steps for graphing the function. graph the function by hand or using a graphing software of your choice (remember to submit the graph).