I am studying AQA further maths gcse and I have two questions concerning functions...
1. How do you work out if a function is increading or decreasing?
2. How do you work out if the range of a function is written as e.g. -2<x<5 or as x<-2 and x>5 ?
Thanks
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Mylifeismaths
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- 27-02-2018 10:06
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Notnek
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- 27-02-2018 10:22
(Original post by Mylifeismaths)
I am studying AQA further maths gcse and I have two questions concerning functions...
1. How do you work out if a function is increading or decreasing?
2. How do you work out if the range of a function is written as e.g. -2<x<5 or as x<-2 and x>5 ?
Thanks
If a function is increasing/decreasing in a certain interval then this means its gradient is positive/negative in that interval so you can use the fact that dy/dx > 0 / dy/dx < 0 and solve the inequality.
If you are asked to show e.g. that a function is an increasing function
then this means its gradient is positive everywhere so you'd need to show that dy/dx > 0 for all x.
If you need more help please post an example question.
2.
Your question is a bit confused. Please post an example. -
Mylifeismaths
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- 27-02-2018 10:44
Thank you for the help on question 1 i know understand it
For the question ... what is the solution to (x+2) (x-1) > 0 how would i know if the answer is either 1. -2<x<1 or 2. x<-2 and x>1 ???? -
Mylifeismaths
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- 27-02-2018 10:45
I done understand either of the questions i have showed.
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RDKGames
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- 27-02-2018 10:54
(Original post by Mylifeismaths)
I done understand either of the questions i have showed.
Similarly, if you're asked about (quadratic)>0 then just look for which x-values the graph is above the x-axis. -
1234123456785678
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- 27-02-2018 11:07
from the graph you could clearly tell that the answer is C since it is the only option where x is larger than -3 and less than 1 (and that is correct if you look at the graph).now, assuming that you have no graph: 1. get the roots of the question (here they are x=-3 and x=1) 2. if the inequality is <0 then you’ll take the range between the roots. if the inequality is >0 you’ll take the range outside the roots. So in this question since it’s <0 you’re gonna take between the roots. so that would be any number that comes after -3 and before 1. any number in that range is definitely larger than -3 but smaller than 1 therefore -3<x<1 which can also be written as x>-3 and x<1
Posted on the TSR App. Download from Apple or Google PlayLast edited by 1234123456785678; 27-02-2018 at 11:13. Reason: TDA Post Edit -
Mylifeismaths
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- 05-03-2018 12:25
Thanks for the help I finally understand it.
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