how many roots of f(x) are rational numbers?\n0\n1\n2\n3

Explanation:

Step1: Identify x - intercepts

The roots of a function (y = f(x)) are the (x) - values where (y=0), i.e., the (x) - intercepts of the graph. From the graph, the (x) - intercepts (where the graph crosses the (x) - axis) are at (x\approx - 0.5), (x = 1), and (x\approx2.5).

Step2: Determine rational roots

A rational number is a number that can be written in the form (\frac{p}{q}) where (p,q\in\mathbb{Z}) and (q\neq0). Among the (x) - intercepts, only (x = 1=\frac{1}{1}) is a rational number. The other two (x) - intercepts ((x\approx - 0.5=-\frac{1}{2}) is an approximation and (x\approx2.5=\frac{5}{2}) is an approximation, and from the graph's precision, we assume non - rational exact values) are likely non - rational in the exact sense. So there is 1 rational root.

Answer:

1