Problem preview

F-BF.1.a Warmup M2-014-A12-V02

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

Write an explicit function model from a context and choose a reasonable domain

Problem

Use the rectangle diagram to define \(x\) as the width in feet and write \(A(x)=x(x+5)\) square feet. Solve both positive-length inequalities, state the continuous contextual domain, and explain why the degenerate boundary is excluded.

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A(x) = x(x + 5) square feet, where x is a length in feet. Both side lengths must be positive, so the continuous domain is x ∈ (0, ∞).

A(x) = x(x + 5) for all real x. Negative side lengths are not physically meaningful.

A(x) = x(x + 5) square feet, where x is in feet. No restrictions or contextual domain are given.

The domain is [−5, ∞) because x + 5 ≥ 0. This includes nonpositive widths x.

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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 context and choose a reasonable domain