Uganda NCDC Lesson Plans

Evaluating Functions
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S4 Mathematics - Term 1

Topic 1: Composite Functions

Lesson 3: Evaluating Functions

Duration: 40 minutes

Learning Outcomes

By the end of this lesson, you should be able to:

  • Evaluate functions with various types of rules
  • Work with quadratic and cubic functions
  • Solve problems involving function evaluation

Warm-Up: Quick Review

Solve in your exercise book:

  1. f(x) = 5x, find f(4)
  2. g(x) = x - 7, find g(10)
  3. h(x) = 2x + 3, find h(5)

Warm-Up Answers

  1. f(4) = 5(4) = 20

  2. g(10) = 10 - 7 = 3

  3. h(5) = 2(5) + 3 = 10 + 3 = 13

Today: More Complex Functions

We will work with:

  • Quadratic functions (involving x²)
  • Cubic functions (involving x³)
  • Problem-solving with functions

Quadratic Functions

f(x) = x²

This function squares the input.

Example:

  • f(3) = 3² = 9
  • f(5) = 5² = 25

Squaring Negative Numbers

f(x) = x²

  • f(-2) = (-2)² = 4
  • f(-3) = (-3)² = 9

Key point: Squaring a negative gives a positive!

More Complex Quadratic

g(x) = x² + 1

Find g(3):

  • g(3) = 3² + 1
  • g(3) = 9 + 1
  • g(3) = 10

Practice: g(x) = x² + 1

Find g(4):

  • g(4) = 4² + 1
  • g(4) = 16 + 1
  • g(4) = 17

Cubic Functions

From the NCDC curriculum:

f(x) = 2x³

This multiplies 2 by x cubed.

Evaluating f(x) = 2x³

Find f(2):

  1. Calculate 2³ = 8
  2. Multiply by 2: 2 × 8 = 16

f(2) = 16

More Examples: f(x) = 2x³

Find f(3):

  1. Calculate 3³ = 27
  2. Multiply by 2: 2 × 27 = 54

f(3) = 54

Step-by-Step Evaluation

Evaluating cubic function

Pair Practice

Given: f(x) = 2x³

Find:

  • f(1) = ?
  • f(-1) = ?
  • f(4) = ?

Work with your partner (2 minutes)

Answers: f(x) = 2x³

  • f(1) = 2(1³) = 2(1) = 2

  • f(-1) = 2(-1)³ = 2(-1) = -2

  • f(4) = 2(4³) = 2(64) = 128

Remember BODMAS!

Brackets
Orders (powers)
Division
Multiplication
Addition
Subtraction

Calculate powers FIRST, then multiply!

Problem Solving: Forward

h(x) = 3x - 2

"If the input is 5, what is the output?"

h(5) = 3(5) - 2 = 15 - 2 = 13

Problem Solving: Reverse

h(x) = 3x - 2

"If h(a) = 10, what is a?"

This means: 3a - 2 = 10

Solving for the Input

3a - 2 = 10

Add 2 to both sides:
3a = 12

Divide by 3:
a = 4

Check Your Answer

Verify: h(4) = 3(4) - 2 = 12 - 2 = 10 ✓

When h(a) = 10, a = 4

Curriculum Example

From NCDC:

  • f(x) = 6x
  • g(x) = x + 5

Find:

  • f(3) = 6(3) = 18
  • g(3) = 3 + 5 = 8

Building a Table

f(x) = 2x

x f(x) = 2x
1 2
2 4
3 6
4 8
5 10

What Pattern Do You See?

x f(x) = 2x
1 2
2 4
3 6
4 8
5 10

The outputs are the even numbers!

Summary: Types of Functions

Type Example Key Operation
Linear f(x) = 3x + 2 Multiply and add
Quadratic f(x) = x² Square
Cubic f(x) = 2x³ Cube and multiply

Summary: Key Skills

  1. Substitute the input for x
  2. Follow BODMAS for order of operations
  3. Calculate step by step
  4. Check by substituting back

Exit Questions

  1. Given f(x) = x² - 1, find f(4)
  2. Given g(x) = 2x³, find g(2)
  3. If h(x) = 4x and h(a) = 20, find a

Answers to Exit Questions

  1. f(4) = 4² - 1 = 16 - 1 = 15

  2. g(2) = 2(2³) = 2(8) = 16

  3. 4a = 20, so a = 5

Homework

  1. f(x) = x²: Find f(6), f(-3), f(0)

  2. g(x) = 3x + 4: Find g(2), g(5), g(-1)

  3. h(x) = x² + x: Find h(3), h(4), h(5)

  4. If f(x) = 5x and f(a) = 35, find a

Next Lesson

Lesson 4: Functions Review and Transition to Composites

We will:

  • Review all function concepts
  • Prepare for composite functions
  • Practice with multiple functions together

Credits

Created: December 2025
Based on: NCDC Lower Secondary Mathematics Syllabus (2019)

Source: National Curriculum Development Centre (NCDC), Uganda