# two intersection points but only shows one?

Mads Frederik Toft shared this question 1 year ago

If I have two very basic functions f(x) = sqrt(x) and g(x) = 0.5*x they intersect in x = 0 and x = 4.

I can get Geogebra to show them if I use the intersection tool, however I use intersect command it only shows one of them. So my question is how do I get it to show both points using the intersect command? 1

Seems to be a bug

Lets say

X=solutions(f=g)

Y=(X,f(X))

Meanwhile ... 3

l2 = {Intersect(g, f, -1, 5)}→ only {(4, 2)}.

Intersect( <Function>, <Function>, <Start x-Value>, <End x-Value> )

You must specify search intervals

In (0,0), the intersection does not want to be defined. If you specifically set: A = Intersect(g, f, (0, 0))→(0,0)!!!!!

in the case: h(x) = If(x ≥ 0, f(x), x)→l6 = {Intersect(g, h, -1, 5)}→ {(0, 0), (4, 2)} !!! 1

@Roman, Thank your for your answer The tricky is to try to teach this to high school level students. So I whish the guys and girls coding geogebra would attempt if possible to include this in the intersect tool :) 2

intersect use methods of Bolzano , Newton or tangent

try solutions(f(x)=g(x)) in CAS view for no numeric solutions 2

Click with the Intersect Tool at each intersection point