Sec 3 Term 3
Unit 12 : Standard Graphs

Starter:

1. Graphs of y = ax, where a is constant.
Click on this link to recap on the straight line.
Click on this applet and investigate the effect of a on the graphs.
Conclusion :
When a > 0, it is a straight line with positive gradient and the y-intercept = 0.
When a < 0, it is a straight line with negative gradient and the y-intercept = 0.

2. Graphs of y = ax^2
Click on this applet and investigate the effect of a on the graphs.
Conclusion:
When a >0, it is a quadratic curve with a "U" shape (min. point) and the min. pt. = (0,0).
When a <0, it is a quadratic curve with a "n" shape (max. point) and the max. pt. = (0,0).

3. Graphs of y =ax^3
Click on this applet and investigate the effect of a.

4. Graphs of y = a/ x
Click on this link and investigate the effect of a.

5. Graphs of y = a/ (x^2)
Now, you are on your journey to create the applet for graphs of this form. Follow the instruction carefully. Click on this link : www.geogebra.org to download the software and you are ready to create an interactive applet here.

Step 1: Load geogebra.

Step 2: Click on the slider and create the slider for a.
reciprocal 1
reciprocal 1



Step 3: Input into the input bar : y = a/x^2

reciprocal 2
reciprocal 2


Step 4: Save this applet as Applet 1
6.1) Graph of y =k(a^x), k>0 and a > 1.
Step 1: Load geogebra

Step 2: Create slider k where k ranges from -5 to 5 in interval of 0.1 and slider a where a range from 1.1 to 10 and in interval of 1.
exponential pic 1
exponential pic 1


Step 3: At the input bar enter this : y = k*a^x

exponential pic 2
exponential pic 2


Step 4: Save this applet as Applet 2.

6.2) Graph of y =k(a^-x), k>0 and a > 1.
Create another applet for this form of graph.

7.) Graphs of y =a(x^n) where n = 1/2 and n = 1/3.
Create another applet of this form of the graph.

8.) Graphs of y^2 = kx, k>0 and k <0.
Create an interactive applet to discover more on this family of graphs.
y square
y square


Main Course:
a) After you have created all the applets, you may now proceed to complete the slides on this unit.


b) Now, you should be equipped with the knowledge of the various types of curves and their tansformations.
You must complete this set of examples in the notes.

c) You may proceed to the textbook exercise for this unit.
Homework : Exercise 9.1 (pg 189) Q2, Q4, Q8, Q10
Dessert:
Congratulation! You have completed the content required for this unit.
Now, you must complete this assignment.
a) Assignment :

b) Play this cannon game below to ensure that you have attained absolute understanding of this unit.

ScreenShootStandard graph
ScreenShootStandard graph