Problem

Contrast the algebraic and contextual domains of \(A(w)=w(14-w)\) for a nondegenerate garden. State the unrestricted polynomial domain, solve \(\text{both}~\text{positive}\text{-}\text{length}~\text{inequalities}\), give the intersection in meters, and explain why widths \(0\) and \(14\) are excluded.

Neutral domain-comparison card. It contains no graph, contextual interval, endpoint status, or answer information.

Answer choices

Choose your path.

Preview only

algebraic/unrestricted domain=(-∞,∞); contextual constraints=w>0 and14−w>0; intersection=0<w<14; contextual domain=(0,14) meters; endpoint status=0,14 excluded as degenerate zero-width cases

algebraic/unrestricted domain=(-∞,∞); contextual constraints=w>0 only; intersection=w>0; contextual domain=(0,∞) meters; endpoint status=0 excluded and no upper endpoint; retained graph=all points with positive width

algebraic/unrestricted domain=(0,14); contextual constraints=w>0 and14−w>0; intersection=0<w<14; contextual domain=(0,14) meters; endpoint status=both excluded; retained graph=entire parabola

algebraic/unrestricted domain=(-∞,∞); contextual constraints=w≥0 and14−w≥0; intersection=0≤w≤14; contextual domain=[0,14] meters; endpoint status=both included as zero-area gardens; retained graph=closed segment between the intercepts

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.