function analysis

Practise function analysis with an original VectorPaths question, worked explanation and related VCE Methods practice.

1 practice marks

Original practice question

A rectangle has width $a$ and height $6 - 2a$. Explain why $0 < a < 3$ must hold for the area of the rectangle to be positive.

Worked explanation

• Analyze positive area conditions

  \[a > 0 \text{ and } 6 - 2a > 0 \implies 0 < a < 3\]

Area = $a(6 - 2a)$. For area > 0, need $a > 0$ and $6 - 2a > 0$, giving $0 < a < 3$.

Original VectorPaths practice; not an official VCAA question or marking rubric.