Question

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

• A. 0
• B. 1
• C. 2
• D. 4

Hint:

Always ensure you look at intersections only on the $x$-axis for $y = f(x)$.
If the graph were instead given as $x = f(y)$, then you would look for the intersections on the $y$-axis.

Answer 1

The Correct Option is C

A zero of $f(x)$ is any value of $x$ where the graph actually touches or crosses the horizontal $x$-axis, since that is where $y = f(x) = 0$. Let us check the given options against the graph instead of just counting crossings directly.

1. 0: This would mean the curve never meets the $x$-axis anywhere. The graph clearly dips down and comes back up across the axis, so this is wrong.
2. 1: This would mean the curve touches the axis at a single point without crossing through it (like the graph just grazing the axis). That is not what the given curve does.
3. 2: The curve crosses the $x$-axis at two separate points as we trace it from left to right, once on the way down and once on the way back up.
4. 4: This would need four separate crossing points, which is more than what the graph shows.

The graph also crosses the $y$-axis at one point, but that crossing tells us the value of $f(0)$, not a zero of the function, so it is not counted here.

Let's summarize:

• A zero of $f(x)$ is an $x$-axis crossing point only.
• The given curve crosses the $x$-axis at exactly 2 points.

So the number of zeroes of $f(x)$ is 2, which corresponds to option (C).

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