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

Step 1: Understanding the Concept:
The zeroes of a polynomial function \(f(x)\) are the values of \(x\) for which \(f(x) = 0\).
Geometrically, these are the points where the graph of \(y = f(x)\) intersects or touches the \(x\)-axis.
Step 2: Key Formula or Approach:
Count the total number of distinct points where the curve crosses or meets the horizontal \(x\)-axis.
Step 3: Detailed Explanation:
Looking at the provided graph:
1. The curve crosses the \(x\)-axis once on the negative side (left of the origin).
2. The curve passes through the origin \((0,0)\), which is a point on the \(x\)-axis.
3. The curve crosses the \(x\)-axis once on the positive side (right of the origin).
Total points of intersection = \(1 + 1 + 1 = 3\).
Step 4: Final Answer:
Since the graph intersects the \(x\)-axis at 3 distinct points, the number of zeroes of \(f(x)\) is 3.