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March 29, 2024, 05:50:34 pm

Author Topic: How to sketch any function  (Read 1798 times)

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jasmine383

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How to sketch any function
« on: September 08, 2020, 09:59:38 am »
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Hi everyone, hope your studies are going well ;)

Do you guys have any tips for sketching? A particular order to do things?

Everytime I try to sketch, it just comes out wrong and I've lost motivation towards all sketching questions.
Any help would be much appreciated! 

If you want an example, how would you sketch: y=x^2-x^3

Bri MT

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Re: How to sketch any function
« Reply #1 on: September 08, 2020, 11:09:21 am »
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Hey!

When I look at a function for graphing I approach it like this:
1. What family of functions does it belong to?
2. What are the co-ordinates of key features?
3. Graph

For your example:
1.  This is a cubic graph, so I'm expecting either a point of inflection or two turning points

2. 
a) All cubics have a y-intercept. Like other graphs, we find this by setting x = 0. ( y = 0 - 0 = 0 )
b) All cubics at least 1 x intercept. 0 = -x^3 + x^2 = x^2(-x + 1), x = 0, 1

3. We graph, starting in the top left and heading down to "bounce" off the origin then cutting through at x = 1.  This considers: x^3 having a negative coefficient (for direction) and in the factorised form (x-0)^2 meaning that 0 is a "bounce" point.  Alternatively, you could find the stationary points by differentiating the function to see how it "turns".

Hope this helps :)

Edit: to know which families of functions to know check the study design :)

jasmine383

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Re: How to sketch any function
« Reply #2 on: September 08, 2020, 01:07:53 pm »
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Thanks Bri!

I've just looked at the QCAA syllabus for methods and just realised there are A LOT of functions they expect us to be familiar from Unit 1/2 (but assumed knowledge now for U3/4). I've made a word doc that has all the functions they've specified, but let me know if I've missed any  :)

Jasmine