Problem preview

F-BF.1.a Warmup M2-014-A13-V02

Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.

Write an explicit function model from a verbal situation and evaluate it

Problem

A rectangle has width \(x~\text{units}\) and length \(x+4~\text{units}\). Write its area function \(A(x)\), evaluate \(A(6)\) with the substitution shown, and report the result in square units after checking the two side lengths are physically valid.

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A(x) = x(x + 4) and A(6) = 60 square units. No substitution or contextual check supports the evaluation.

A(x) = x(x + 4). Then A(6) = 6 · 10 = 60, so the area is 60 square units; both side lengths are positive.

A(x) = x(x + 4) and A(6) = 60 x-units. An area output is measured in square units.

A(x) = x + (x + 4), so A(6) = 16 square units. Rectangle area uses the product of side lengths, not their sum.

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Curriculum context

Course: Math II
Standard: F-BF.1.a
Category: Functions
Domain: Building Functions
Objective: Build quadratic and exponential functions from context using explicit formulas, recursive processes, or calculation steps.
Problem type: Write an explicit function model from a verbal situation and evaluate it