WEEK 5 — Functions & Variation Tables

 


Welcome to Week 5 of your eight-week maths catch-up plan.
This week introduces functions, how inputs and outputs work, and how to read a simple variation table (tableau de variation). These ideas appear often in the French curriculum, but they can be made very simple with clear steps.

The video at the top of the page gives you the full lesson.
Below you’ll find the mind map, the day-by-day breakdown, practice exercises, and a short quiz.

Mind Map – Week 5



DAY 1 — What Is a Function?

What to understand

A function is a rule.
It takes an input (antécédent), does something to it, and gives an output (image).

Examples:
• f(x) = x + 3
• f(x) = 2x
• f(x) = x²

Practice

Find:

  1. f(4) for f(x) = x + 3

  2. f(7) for f(x) = 2x

  3. f(5) for f(x) = x²

  4. Fill in a table for f(x) = x + 1 using x = 0, 1, 2, 3

DAY 2 — Function Machines (Input → Output)

What to understand

Think of a function as a machine:

input → rule → output

Example:
If f(x) = x – 2, then f(10) = 8.

Practice

  1. If f(x) = x – 2, find f(9)

  2. If f(x) = 3x, find f(6)

  3. If f(x) = x² + 1, find f(4)

  4. If f(x) = x/2, find f(12)

DAY 3 — Increasing, Decreasing & Constant Functions

What to understand

• If the function gets bigger as x gets bigger → increasing
• If the function gets smaller as x gets bigger → decreasing
• If the function stays the same → constant

Link to y = ax + b:
• a > 0 → increasing
• a < 0 → decreasing
• a = 0 → constant

Practice

Say if each function is increasing, decreasing or constant:

  1. f(x) = 2x + 1

  2. f(x) = –3x + 4

  3. f(x) = 5

  4. f(x) = 0x – 7

DAY 4 — Variation Tables (Tableau de Variation)

What to understand

A variation table shows how a function behaves: rising, falling, or staying flat.

For straight lines:
• f(x) = 2x – 1 → ↑
• f(x) = –x + 3 → ↓
• f(x) = 5 → constant

Practice

Fill in or complete the variation direction:

  1. f(x) = 4x + 3

  2. f(x) = –2x + 5

  3. f(x) = 7

  4. f(x) = x

DAY 5 — Mixed Practice (Revision)

Practice

  1. Find f(8) for f(x) = x + 2

  2. Say if f(x) = –5x + 1 is rising or falling

  3. Fill in a table for f(x) = 2x using x = 0, 1, 2, 3

  4. Identify if f(x) = 0 is constant, rising or falling

Weekly Quiz — Week 5

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(Paste the embed code into HTML view.)

If you're stuck, use the mind map or rewatch the video.

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