Answer: Choice C
[tex]\text{Domain}: 0 \le x \le 55[/tex] and [tex]\text{Average rate of change over domain} = -1.45[/tex] (average rate of change is approximate)
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The domain is the set of allowed x inputs of the function. The smallest x value shown is x = 0, which is from the point (0,80). The largest x value possible is x = 55 from the point (55,0)
The domain is the set of all values between 0 and 55, including both endpoints. Therefore, we get a domain of [tex]0 \le x \le 55[/tex]
Compute the slope of the line through (0,80) and (55,0) to find the average rate of change over the entire function domain.
m = (y2 - y1)/(x2 - x1)
m = (0 - 80)/(55 - 0)
m = -80/55
m = -1.45 approximately
The slope of the line through (0,80) and (55,0) is approximately -1.45, which is also the average rate of change over the entire domain.
Side note: the negative slope or negative rate of change indicates we are going downhill ultimately as we move from left to right.
