Xinmin Secondary SchoolSec 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 = ex y = ex

Asymptote x-axis

y-intercept 1

x-intercept

Sketch

1. Graph B is of the form y = ex. 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 = ex.

3E/AM/IT/Exp&LogGraphs 1

(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 = ex from y = ex.

Graph D E F

Equation y = 2x y = 2x – 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 = 2x – 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)?

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B. LOGARITHMIC GRAPHS

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?

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7. Without using Graphmatica, sketch the following graphs.

(i) y = ln (3 – x).

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.

Summary1. 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.

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