how many roots of f(x) are rational numbers?\n1\n2\n4\n6

Explanation:

Step1: Recall root - definition

The roots of a function (y = f(x)) are the (x) - values where (y = 0), i.e., the (x) - intercepts of the graph of the function.

Step2: Count (x) - intercepts

From the graph, we can see that the graph of (y = f(x)) intersects the (x) - axis at 4 points.

Step3: Analyze rationality of roots

A rational number is a number that can be written as (\frac{p}{q}), where (p) and (q) are integers and (q\neq0). Just by looking at the graph, if the (x) - intercepts are at integer values (which are rational numbers since an integer (n=\frac{n}{1})), we can count the number of rational roots. Since the graph intersects the (x) - axis at 4 distinct points and assuming these points are at rational (x) - values (as no information to the contrary is given), the number of rational roots is 4.

Answer:

4