Interpret key features of rational, square-root, cube-root, and other function models in context.
Audit contextual x- and y-intercepts with units
Problem
For \(P(x)~=~(x~-~5)/(x~+~2)\), where \(x~\ge~0\) is weeks and \(P\) is a unitless profit ratio, find \(\text{both}~\text{intercepts}\), check their feasibility, and interpret each contextual intercept.
Big Picture
What this problem is really about
Treat each intercept as a different question about the same rational model: an x-intercept makes the output zero, while a y-intercept fixes the input at zero. In each case, check that the denominator stays nonzero before interpreting the coordinate. Finish by testing the input against the time domain and attaching the units each axis represents.
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