Create equations in two or more variables, graph them, and interpret relationships with labels and scales.
Interpret a contextual asymptote limit or radical endpoint
Problem
Travel time is \(y~=~120/x\) hours for positive speed \(x~\text{miles}~\text{per}~\text{hour}\). Interpret the vertical asymptote \(x~=~0\) in context.
Big Picture
What this problem is really about
A vertical asymptote is an excluded input boundary, not a point the model reaches. Because speed is positive, examine the reciprocal only as speed approaches the boundary from the right. We’ll track how the quotient behaves as the positive denominator shrinks, then translate that limit into speed and time units while distinguishing approach behavior from an actual value at zero.
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