Question

what does a zero of a graph represent on a coordinate plane? *
the highest point of the graph
the point where the graph crosses the y - axis
the point where the graph crosses the x - axis
the lowest point of the graph
if a function f(x) has a zero at x = 3, what does this mean geometrically? *
the graph crosses the x - axis at the point (3,0)
the graph has a vertical asymptote at x = 3
the graph reaches its maximum value at x = 3
the graph touches the y - axis at (3,0)

Explanation:

A zero of a graph is defined as the x - value for which the function value is zero. Geometrically, on a coordinate - plane, when \(y = 0\), the graph crosses the x - axis. For a function \(f(x)\) with a zero at \(x = 3\), it means \(f(3)=0\), so the point \((3,0)\) is on the graph and the graph crosses the x - axis at this point.

Answer:

1. The point where the graph crosses the x - axis
2. The graph crosses the x - axis at the point \((3,0)\)