LEARN · EXPLAIN · REVISE

State the monotonicity on the real line and justify it.

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

TOPIC 01

Functions: concept and properties: mixed assessment

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

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

01 / Standard#Your turn

f(x)=-9x+2

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

The slope is negative.

Worked solution

Use the definition of the property and keep the domain in view.
Calculate or simplify this relation.
$x_1<x_2\Rightarrow f(x_2)-f(x_1)=-9(x_2-x_1)<0$
The definition compares the outputs at ordered inputs.

Strictly decreasing.

Checks and common pitfalls: The definition compares the outputs at ordered inputs.

Reasoning checklist · self / teacher assessment

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

Teacher preparation and assessment