Relate a function's domain to its graph and to the real-world quantities it describes.
Find the range over a restricted domain
Problem
Over the contextual domain \(0~\le~x~\le~5\), find the range of \(f(x)=2x+3\).
Big Picture
What this problem is really about
The restricted domain supplies inputs, while the range records the outputs those inputs produce. We’ll use the sign of the linear coefficient to determine which domain endpoint gives the minimum and which gives the maximum, evaluate both, and carry over endpoint inclusion. Continuity then tells us whether every output between those extremes is also attained.
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