The document is a lesson plan for teaching logarithmic functions to S4 students, focusing on defining logarithms and their graph characteristics. It includes time allocations, teaching tools such as PowerPoint and worksheets, and class activities aimed at understanding the properties and visual representation of logarithmic functions. Key objectives are for students to sketch graphs and understand the domain and range of logarithmic functions.

1. Lesson Plan: S4 (core) Logarithmic Functions
Lesson Plan
Date N/A Gender Mixed
Duration 40 min Textbook Mathematics in Action (4A)
Class S4 St ability N/A
No. of st. N/A TOPIC Logarithmic Functions
Previous Knowledge:
Students should be able to
1) state the definition of logarithms.
2) apply the properties of logarithm to solve index equations, e.g. 2x = 5x – 1.
3) state the definition of domain and range
Teaching Objective:
Student should be able to
1) state the characteristics of the graph of a logarithmic function.
2) sketch the graph y = loga x, for a > 0 and a ≠ 1.
Teaching Tool(s):
1) Powerpoint (used for whole lesson)
2) Worksheet
Reference:
1) Mathematics in Action (2009), Man, P.F. et al, Pearson
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2. Lesson Plan: S4 (core) Logarithmic Functions
Time Allocation and Teaching contents:
Time (min) Teaching content or activity Objective
3 Introduction
8 Discuss that y = loga x is a function, for a > 1 and a ≠ 0. 2
Review the three ways to describe a function: (1) algebraic
expression (2) tabular representation (3) graphical
representation
Sketch the graph of y = log x and y = log2 x.
Extra note:
Why y = loga x is a function?
Because, for all real x, exist unique y such that y = loga x.
Can refer to the book page 3.6.
Note: Use the Powerpoint. If necessary, excel too.
6 4th class work session: Worksheet 2 – Q1 1
1. Consider the above graphs and answer the following
questions.
a) The graph cuts the x-axis at _________ .
b) The graph _____________________ the y-axis.
c) The value of y is __________ for x > 1.
d) The value of y is __________ for 0 < x < 1.
e) The value of y increases as x ____________ .
f) The rate of increase of y ________ when x
increases.
5 Discuss: 1
Domain of log = +ve real numbers
Range of log = real numbers
The graphs depend on a > 1 or 0 < a < 1 and so are the
characteristics of the graph.
5 Demonstration: 2
e.g.3: Sketch .
y y
(1,0) (1,0)
x x
O O
This graph is shown on page 5.32.
(Show that the graph y = loga x, a > 0 and a ≠ 1 is a reflection
of the graph along x-axis.)
Discussion: Would there be a relationship ?
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3. Lesson Plan: S4 (core) Logarithmic Functions
Pf:
5 Demonstration: 2
e.g.4: Sketch the graph of y = log4 x.
y
y = log2 x
y = log8 x
x
O
[Answer: The dotted-line is the graph of y = log4 x.
Reason: put in the same x (e.g. 64), log8 64 = log8 82 = 2 
log2 64 = log2 26 = 6  log2 64 > log8 64]
Discuss: To get the general relation that for x > 1, if a > b > 1,
the loga x < logb x.
6 5th Class work session: 2
Sketch the graph of and .
2 Summary
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