Maths question help please

Hi, please could I have some help on question 8ii a below. I’m confused on how to find the range. I thought there would be an asymptote at 0 but that’s not the case. Any advice on how to work it out?
Question: https://ibb.co/67WsP766
Thanks!

Hi, please could I have some help on question 8ii a below. I’m confused on how to find the range. I thought there would be an asymptote at 0 but that’s not the case. Any advice on how to work it out?
Question: https://ibb.co/67WsP766
Thanks!

I sketched it and it and I understand the max should be 1 but I'm unsure why the min is zero when the graph doesn't touch the x axis? Thanks

the range shld look like this, (0,1]. ( ) means the range is not inclusive of wtv value is in there. in this case, not inclusive of 0 as there is an asymptote of x=0. [ ] means inclusive of the value, meaning inclusive of 1

but the markscheme says it is inclusive
'State values between 0 and their y-value of maximum point lying in first quadrant M1 accept  or < signs here State correct 0 1  y A1ft following their y-value of maximum point in first quadrant; now with  signs; or equiv perhaps involving g or g( )'

The range shoud be [0,1]. When x=-1/2
g(-1/2) = f(-1/2) = 0
as |0| = 0. g() touches the x-axis at that point whereas f() crosses the x-axis at that point. Just think about the graph of |x| and what happens when x=0.