The graph of \(y = f(x)\) is shown in the figure for some polynomials \(f(x)\). The number of zeroes for the polynomials is
Show Hint
Always look strictly at the x-axis. Intersections with the y-axis do not count towards the real zeroes of \(y = f(x)\).
Since the curve lies entirely in the upper half-plane (above the x-axis), the number of real roots is instantly 0.
Step 1: Recall what a zero of a polynomial looks like on a graph. A zero of $f(x)$ is a value of $x$ where the graph actually meets the x-axis, that is, where $y = 0$. Counting zeroes graphically just means counting these crossing or touching points. Step 2: Read the graph carefully. The curve rises and falls in a wave pattern, but at no point does it come down to touch or cross the horizontal axis. It stays entirely above the x-axis throughout. Step 3: Translate this into a statement about f(x). If the graph never reaches $y = 0$, it means $f(x) > 0$ for every real $x$ shown. There is no real input that makes the output zero. Step 4: Conclude the count of zeroes. Since the graph does not intersect the x-axis anywhere, the polynomial has no real zeroes.
\[ \boxed{0} \]
