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# Gcse further maths Functions watch

1. 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
2. (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
1.

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.

3. 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 ????
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4. I done understand either of the questions i have showed.
5. (Original post by Mylifeismaths)
I done understand either of the questions i have showed.
Since you're kindly given the graph, from that you can observe for which portion of the x-axis is the graph below it. This comes from the fact that if your quadratic is <0 then that means it takes y values which are less than 0, and these are precisely those which lie below the x-axis.

Similarly, if you're asked about (quadratic)>0 then just look for which x-values the graph is above the x-axis.
6. 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
7. Thanks for the help I finally understand it.

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