1. The document provides instructions for sketching exponential and logarithmic graphs. Students are asked to sketch various graphs of exponential and logarithmic functions, noting the shape, asymptotes, and intercepts. 2. Students are asked to describe how changing components of exponential and logarithmic equations, such as coefficients and signs, affects the graphs. 3. The objectives are for students to be able to sketch exponential and logarithmic graphs accurately, including asymptotes and intercepts, and draw straight lines to solve equations.

1. Xinmin Secondary School
Sec 3E A Maths IT Worksheet
Topic: Graphs of Exponential and Logarithmic Functions
Name: ( ) Class: Date:
Objectives: At the end of the lesson, you should be able to
1. sketch exponential graphs, indicating clearly the asymptotes & intercepts.
2. sketch logarithmic graphs, indicating clearly the asymptotes & intercepts.
3. draw the straight lines required to solve equations.
Instructions:
1. In Graphmatica, under the View menu, ensure that Rectangular is selected.
2. For each of the following graphs, focus on the following:
 shape
 asymptote
 axes intercepts, if any.
3. Deduce relationships among graphs.
A. EXPONENTIAL GRAPHS
Graph A B C
Equation y = ex y = e− x y = − ex
Asymptote x-axis
y-intercept 1
x-intercept 
Sketch
1. Graph B is of the form y = e−x. Describe how you can obtain this graph from y = ex (Graph A)?
2. Graph C is of the form y = −ex. Describe how you can obtain this graph from y = ex (Graph A)?
3. Why do you think the x-axis is the asymptote in the above graphs?
4. Without using Graphmatica, sketch the graph of y = −e−x.
3E/AM/IT/Exp&LogGraphs 1

2. (a) Asymptote :
(b) y-intercept :
(c) x-intercept :
To verify your answer, use Graphmatica to plot the above graph. Describe how you obtained the graph
of y = −e−x from y = ex.
Graph D E F
Equation y = 2x y = 2− x – 1 y = − 2x + 3
Asymptote
y-intercept
x-intercept
Sketch
1. Graph D has the same shape, asymptote and intercept as Graph A? Why is that so?
2. Graph E is of the form y = 2−x – 1. Describe how you can obtain this graph from y = 2x (Graph D)?
3. Graph F is of the form y = −2x + 3. Describe how you can obtain this graph from y = 2x (Graph D)?
B. LOGARITHMIC GRAPHS
3E/AM/IT/Exp&LogGraphs 2

3. Graph A B C D
Equation y = lg x y = lg (− x) y = − lg x y = − lg (− x)
Asymptote
y-intercept
x-intercept
Sketch
1. Graph B is of the form y = lg (−x). Describe how you can obtain this graph from y = lg x (Graph A)?
2. Graph C is of the form y = − lg x. Describe how you can obtain this graph from y = lg x (Graph A)?
3. Graph D is of the form y = −lg (−x). Describe how you can obtain this graph from y = lg x (Graph A)?
4. When the coefficient of x in an equation changes from positive to negative, what do you notice about
the change in the graphs?
5. When an equation changes from positive y to negative y, what do you notice about the change in the
graphs?
6. Do you expect any difference in the shape, asymptote and intercept of the graphs of y = lg x and
y = ln x? Why?
7. Without using Graphmatica, sketch the following graphs.
(i) y = ln (3 – x).
3E/AM/IT/Exp&LogGraphs 3

4. To find asymptote: Let (3 – x) = 0
x= .
To find x-intercept: Let ln(3 – x) = 0
(3 – x) = 1
x= .
(ii) y = 1 – ln (x + 2)
To find asymptote: Let (x + 2) = 0
x=.
To find x-intercept: Let 1 – ln (x + 2) = 0
ln (x + 2) = 1
x + 2 = e1
x= .
To find y-intercept:: x = 0 ∴ y = .
To verify your answers, use Graphmatica to plot the above graphs.
Summary
1. In sketching exponential and logarithmic graphs, focus on the
(i)
(ii)
(iii)
2. When the coefficient of x in an equation changes from positive to negative, the
graphs are a reflection of each other in the -axis.
3. When an equation changes from positive y to negative y, the graphs are a reflection
of each other in the -axis.
3E/AM/IT/Exp&LogGraphs 4