1.3.5—Graph intersections

An intersection of y=f(x) and y=g(x) has f(x)=g(x); solve for x, then substitute to find y. The number of real roots gives the number of intersections.

Factorisation may reveal exact roots; otherwise use a graph or numerical method only after locating intervals. Reject roots outside the domain or interval shown.

For y=x² and y=2x+3, x²=2x+3 gives x=3 or −1, producing points (3,9) and (−1,1).

Solving f(x)=g(x) finds x-coordinates only; reporting roots without their corresponding y-values is not a complete intersection answer.