Question

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

• A. 0
• B. 1
• C. 2
• D. 3

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.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The "zeroes" of a function \( f(x) \) are the values of \( x \) for which \( f(x) = 0 \). Geometrically, these correspond to the points where the graph of the function intersects the \( x \)-axis.
Step 2: Key Formula or Approach:
Count the number of intersection points between the curve and the horizontal \( x \)-axis.
Step 3: Detailed Explanation:
1. Based on the description: - Intersection 1: Left of the origin. - Intersection 2: At/near the origin. - Intersection 3: Right of the origin. 2. Total points of contact with the \( x \)-axis = 3.
Step 4: Final Answer:
The number of zeroes of \( f(x) \) is 3.