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
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