The graph of y = f(x) is given. The number of zeroes of f(x) is :
Show Hint
If a graph "touches" the x-axis (turns back) without crossing, it still counts as a zero (a repeated root). Always count every point where the graph meets the axis.
The problem requires us to find the number of zeroes of the function \(y = f(x)\) based on the given graph. A zero of a function is a point where the graph intersects the x-axis, i.e., where \(f(x) = 0\).
Let's analyze the graph to determine how many times it crosses the x-axis:
Point 1: The graph crosses the x-axis at this point, indicating a zero of the function.
Point 2: The graph crosses the x-axis at this additional point, indicating another zero.
Point 3: The graph crosses the x-axis once again, providing a third zero.
Thus, the graph crosses the x-axis at three distinct points.
Conclusion: The function \(f(x)\) has three zeroes. Therefore, the correct answer is 3.
