C3 Modulus functions

Dear Maths Genius,

I am writing because i have a problem with drawing modulus functions on the same graph. When you look at the question, I try to draw the functions as accurately as I can but i still miss out one intersection point.

I have attached the pictures to the question I did in the edexcel and the mistake I made. Please i want to know if there are anhy tips on how to draw the functions probably without missing out any points of intersections.

Thank you very much.

mod q .jpg

Attachment not found

Original post by bigmansouf

...

You can find all the points of intersection by realising that

\lvert x\rvert = \lvert -4x-5 \rvert \rightarrow \pm x=\pm(-4x-5)

which gives you 4 linear equations to solve:

x=(-4x-5) ... (1)

x=-(-4x-5) ... (2)

-x=(-4x-5) ... (3)

-x=-(-4x-5) ... (4)

but you may notice that (1)=(4) and (2)=(3) which leaves you only with 2 equations to solve therefore this shows that for any two moduli of two linear functions there can be a maximum of 2 intersections.

Once you have the intersections, along with where the minimum points, you can work from there to draw them. However also take into account the gradients which can help you draw the graphs accurately together, as one will have steeper lines than the other.

(edited 7 years ago)

Reply 2

B_9710

18

For x>-5/4 you have sketched y=4x+5 as having a lower gradient than y=x which of course is not true.

Reply 3

bigmansouf

OP

20

Original post by RDKGames

You can find all the points of intersection by realising that

\lvert x\rvert = \lvert -4x-5 \rvert \rightarrow \pm x=\pm(-4x-5)

which gives you 4 linear equations to solve:

x=(-4x-5) ... (1)

x=-(-4x-5) ... (2)

-x=(-4x-5) ... (3)

-x=-(-4x-5) ... (4)

but you may notice that (1)=(4) and (2)=(3) which leaves you only with 2 equations to solve therefore this shows that for any two moduli of two linear functions there can be a maximum of 2 intersections.

Once you have the intersections, along with where the minimum points, you can work from there to draw them. However also take into account the gradients which can help you draw the graphs accurately together, as one will have steeper lines than the other.