Kenneth ChengMathematical modeling
← Senior Mathematics Studio

LEARN · EXPLAIN · REVISE

How does adding a constant affect monotonicity? Prove your answer.

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

Return to the lesson / paper ↗

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 / Foundation#Your turn

How does adding a constant affect monotonicity? Prove your answer.

g(x)=f(x)+8g(x)=f(x)+8
  • Use the domain, units and sampling assumptions stated in the question.
Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1
Use the definition of the property and keep the domain in view.
Hint 2
Compare two outputs by subtraction.
Worked solution

  1. Use the definition of the property and keep the domain in view.

  2. Calculate or simplify this relation.

    g(x2)−g(x1)=f(x2)−f(x1)g(x_2)-g(x_1)=f(x_2)-f(x_1)

  3. The constant cancels from every output difference.

It preserves increasing or decreasing behaviour.

Checks and common pitfalls: The constant cancels from every output difference.

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 ↗