f(x)=|x|,g(x)=ax+ 1
The root of solving the equation is to find the abscissa of the intersection of two functions.
Through images
If there is a positive root but no negative root, it means x0 >;; 0, and should only intersect the positive semi-axis part of f(x).
F(x) passes through the point (0, 1).
Therefore, the slope a of g(x) must be compared with the slope of y =-x.
That is, a≤- 1