AIBU to ask for help with a Maths question?

[MathWhizz]

DD is doing A-Level Maths and is struggling with question 9 C on the attached photo of her worksheet. It's about Modulus Functions.

Can anybody help at all?

Thanks for any ideas!

Sorry, forgot to attach picture

Still no picture?

Ah I seen now.

The modulus is saying the value but positive, it can’t be negative. So part a for example would mirror the part below the x axis up above it, so it would make a W shape

So he: if y=Fx = -1 then then y=|fx|=1
Like this

FTEngineerM has given the answer, but I'd be wondering a bit about why DD couldn't do it. Does she not understand modulus, in which case she needs to learn that. Or was it that she couldn't get her head round how to use it in a practical situation? That's more of a problem, since maths at A-level and higher is about using your knowledge to apply to unknown situations. Did she manage to draw f(-x) without help?

@FTEngineerM

So he: if y=Fx = -1 then then y=|fx|=1 Like this

Perfect name

Well to plot y = |f(x)| you just need to reflect the portion of the lines which go below the x axis (i.e. to the left of x=-1 and to the right of R). the rest stays the same.

To ploty = f(-x) you need to reflect in the y-axis so it will now cross the x-axis at 3 and -R. but it will still cross the y-axis at the same point. The point P is now to the right of the y-axis.

The equation of the f(x) = 2 - |x+1| the point P occurs when x+1 = 0 i.e. x=-1 and f(x) = 2 so has coordinates (-1,2)

The points to the right of the point P represents points for which x+1 is positive so has equation y = 2-(x+1) i.e. y = 1-x. Ot crosses the y-axis at (0,1) and x-axis at (1,0). So Q is (0,1) and r is (1,0)

Sorry first comment should say reflect in the y-axis to the left of x=-3 and to the right of R. so you get a zig zag like PP drew above.

@FTEngineerM Thank you for your posts. She is still a bit baffled. I will try and book an online Maths tutor lesson to try and help her with the basic principles. Hopefully that should help.

@IMNOTSHOUTING Thank you for your posts. I will show them to DD and will hopefully make things clearer!

Some of the above responses relate more to earlier parts of the question, though you need to understand the earlier parts to have a hope of answering part (c).

Happy to explain in more detail if she needs!

Thank you, IMNOTSHOUTING. You possibly did A level maths less than 40 years ago!

Try this website:
www.ixl.com
You can subscribe but also use it for free. It’s excellent!

To find point P:
This is the max value reached by the function. Since |x+1| is never negative, this will occur when x+1 =0. ie x=-1, y=2, so P is the point (-1,2)
To find point Q:
When x=0, f(x)=2-|0+1|=1 so Q is the point (0,1)
To find point R:
f(x)=0 if 2-|x+1|=0, so 2=|x+1|. This happens when x=1 and when x= -3, so R is the point (1,0).

@CasperGutman Thank you. DD has now understood how to do the question after reading your post. That's brilliant!