Kenneth ChengMathematical modeling
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Find the greatest value on the stated closed interval.

Read the idea, work independently, then explain what changed.

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TOPIC 01

Functions: concept and properties: mixed assessment

A mixed assessment: identify the method, justify it and revise your reasoning.

What you will be able to explain

  • Connect the chapter skills without relying on the order of the exercises.

Try it. Leave your reasoning visible.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Your turn

Find the greatest value on the stated closed interval.

f(x)=(x−10)2;x∈[9,13]f(x)=(x-10)^2;\quad x\in[9,13]
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Identify the input domain, rule and requested output before substituting.
Hint 2
Compare the vertex and both endpoints.
Worked solution

  1. Identify the input domain, rule and requested output before substituting.

  2. Calculate or simplify this relation.

    f(9)=1,f(10)=0,f(13)=9f(9)=1,\quad f(10)=0,\quad f(13)=9

  3. The greatest distance from the vertex determines the maximum here.

The requested value is 9.

Checks and common pitfalls: The greatest distance from the vertex determines the maximum here.

Think first. Reveal a hint when the class is ready.

Focus on one question

Teacher preparation and assessment

Question sequence

  • Ask students to name the relevant condition before calculating.

Board plan

  • Compare valid methods and annotate their conditions.

Anticipated thinking

  • A correct final value may still hide a missing assumption.

Assessment checklist

  • Check the method, conditions, reasoning and interpretation separately.

No sign-in. Work stays in this browser. Export before clearing browser data. Written reasoning is assessed with a checklist.

Curriculum and source notes ↗