lesson plan for teaching the relationship between the bases of iogarithmic functions and their graphical representation.

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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