During swim practice, an Olympic swimmer is required to complete three swimming intervals, in this order: warm-up freestyle, sprint freestyle, and cool-down breast stroke. After he completes each interval, he rests for three minutes. Sketch a graph that represents the swimmers’ interval times with respect to swimming speed. Assign the x- and y-axes with appropriate labels. You may use description words instead of numbers to label the graph.

I'm not sure if the warm up speed is less than the cool down speed.  If it is different than how I did it you just need to swap their positions on the y axis, so the "lumps" or whatever you want to call the shapes will be in opposite positions.  The middle one will stay the same because it is the fastest and in between the two happening.  Also let me know if you can't read any of the labels

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.

the answer is a

step-by-step explanation: