# Curve sketching

Hello Bruce,

I have this question here Q5 - https://pastpapers.co/cie/IGCSE/Mathematics-International-0607/2021-Oct-Nov/0607_w21_qp_41.pdf

m is negative when the function is decreasing. The answers given say that the function is decreasing only from –1 < x < 0.208
However, at the other two ends of the graph x<-1 the function decreased when it is reaching x = -1 and in x>2, after reaching the point where the curve turns and heads towards the asymptote, the function is decreasing as well.
Why is that portion not considered?

Thanks

Sorry, here “after reaching the point where the curve turns and heads towards the asymptote, the function is decreasing as well.” the function is increasing.

Here’s a Desmos graph of the function so everyone can see what we’re talking about:

I agree that the function’s curve has negative slope for -7 \le x \lt -1, in addition to the region in the upper part of the graph you cite. I also don’t see a reason to ignore that left part, and can’t tell you why your “official answer” didn’t include it.

Sorry, here “after reaching the point where the curve turns and heads towards the asymptote, the function is decreasing as well.” the function is increasing.

Assuming you mean that for 2 \lt x \lt 7 the function is increasing, then agreed.