Problem

Interpret $C(h)=30(h-2)+90$ for $h\ge~2$ by giving its anchor, the meaning of $h-2$, its rate and contextual domain, its expanded form, and a check at $h=5$.

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A shifted linear form is anchored at the input that makes its parenthesized expression zero. We’ll interpret that anchor, the number of units beyond it, and the rate applied to those additional units, while respecting the stated domain. Expanding the rule and checking another input will confirm the algebra without turning an out-of-domain intercept into a contextual starting value.

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anchor = C(2)=$90; shifted input = h-2 counts billable hours; rate = $30/hour; domain = h≥2; expanded form = 30h+30; check = C(5)=$150

anchor = C(2)=$90; shifted input = h-2 counts billable hours beyond the first 2; rate = $30 per additional hour; domain = h≥2, so expanded y-intercept is not the contextual start; expanded form = C(h)=30h+30; check = C(5)=$180

anchor = C(0)=$30; shifted input = h-2 subtracts $2 from cost; rate = $30/hour; domain = h≥2; expanded form = 30h+30; check = C(5)=$180

anchor = C(2)=$90; shifted input = h-2 counts billable hours; rate = $30/hour; domain = all h≥0 with expanded intercept as actual start; expanded form = 30h+30; check = C(0)=$30

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Interpret \(C(h)=30(h-2)+90\) for \(h\ge~2\) by giving its anchor, the meaning of \(h-2\), its rate and contextual domain, its expanded form, and a check at \(h=5\).

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