Hey there! Sign in to join this conversationNew here? Join for free
x Turn on thread page Beta
    • Thread Starter
    Offline

    2
    ReputationRep:
    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
    • Community Assistant
    • Study Helper
    Offline

    20
    ReputationRep:
    Community Assistant
    Study Helper
    (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.

    Your question is a bit confused. Please post an example.
    • Thread Starter
    Offline

    2
    ReputationRep:
    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 ????
    Attached Images
     
    • Thread Starter
    Offline

    2
    ReputationRep:
    I done understand either of the questions i have showed.
    • Community Assistant
    Offline

    20
    ReputationRep:
    Community Assistant
    (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.
    Offline

    6
    ReputationRep:
    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 Play
    • Thread Starter
    Offline

    2
    ReputationRep:
    Thanks for the help I finally understand it.
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: March 5, 2018
Poll
Do you like carrot cake?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.