Question

The graph of \(y = f(x)\) is given. The number of zeroes of \(f(x)\) is :

• A. 0
• B. 1
• C. 3
• D. 2

Hint:

Always look specifically at the \(x\)-axis intersections. Intersections with the \(y\)-axis represent the value \(f(0)\) and are not considered zeroes of the function.

Answer 1

The Correct Option is C

To determine the number of zeroes of the function \(y = f(x)\), we need to find the points where the graph of the function intersects the x-axis.

The x-axis represents the line \(y = 0\). Therefore, the zeroes of the function are the x-values where \(f(x) = 0\).

From the graph, observe the points where the curve intersects the x-axis:

1. There is an intersection at one point to the left of the origin.
2. There is an intersection at the origin itself.
3. There is another intersection to the right of the origin.

Thus, the function \(f(x)\) has three zeroes because it intersects the x-axis at three distinct points.

Therefore, the correct answer is 3.