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# Exp&log graphs it worksheet

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### Exp&log graphs it worksheet

1. 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. 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. 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. 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