The graph of the given polynomial function indicates three rational zeros. The Rational Zeros Theorem can be used to find the exact values of these zeros.
The graph of the polynomial function f(x) = 3x^3 + ax^2 + bx -15 shows that the polynomial has three rational zeros. We can find the exact values of these zeros by using the Rational Zeros Theorem. According to the theorem, if a polynomial has a rational zero, it can be written as a fraction of two integers, where the numerator is a factor of the constant term (-15) and the denominator is a factor of the leading coefficient (3).
To find the possible rational zeros, we need to list the factors of both the constant term (-15) and the leading coefficient (3). In this case, the factors of -15 are 1, -1, 3, -3, 5, -5, 15, and -15. The factors of 3 are 1 and 3.
By testing these possible zeros using synthetic division or direct substitution, we can determine the exact values of the rational zeros of the function.