1. The problem is to find the points where two functions intersect, which means finding the points where their values are equal. 2. To find intersection points, set the two functions equal to each other: if the functions are $f(x)$ and $g(x)$, solve $f(x) = g(x)$. 3. This equation may be solved by algebraic manipulation: simplifying, factoring, or using numerical methods if necessary. 4. If the functions do not cross, it means there are no real solutions to $f(x) = g(x)$. 5. To verify, you can check the difference $h(x) = f(x) - g(x)$ and see if it ever equals zero. 6. If $h(x)$ never equals zero, the graphs do not intersect. 7. Sometimes graphs appear close but do not cross; this is confirmed by solving the equation and finding no real roots. 8. In summary, finding intersection points requires solving $f(x) = g(x)$ and checking for real solutions.