Kenneth ChengMathematical modeling
← Senior Mathematics Studio

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Recover f(x) from the shifted-input identity.

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 / Standard#Your turn

Recover f(x) from the shifted-input identity.

f(x+9)=2x+3f(x+9)=2x+3
  • 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
Introduce a new variable for the complete input.
Worked solution

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

  2. Calculate or simplify this relation.

    t=x+9;f(t)=2(t−9)+3t=x+9;\quad f(t)=2(t-9)+3

  3. Renaming the dummy variable does not change the function.

f(x)=2x−15.

Checks and common pitfalls: Renaming the dummy variable does not change the function.

Reasoning checklist · self / teacher assessment
  • State the relevant definition, condition or model.
  • Show a valid calculation, proof or counterexample.
  • Interpret the conclusion with its restrictions.

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 ↗