Question 883389
Rational root theorem only tells you that if you have real roots, they are rational roots of the form p/q. However they don't tell you anything else about the behavior of the function.
The maximum number of real zeros that a function can have is equal to the degree of the polynomial. The real zeros and the x-intercept are the same thing so for a cubic polynomial which has degree 3, the maximum number of zeros and intercepts is 3. Similarly the maximum number of turning points is always 1 less than the degree. 
So you're looking for 3,3,2.
{{{graph(300,300,-3,3,-100,100,7x^3+4x^2-3x+3)}}}
In this case, there is only one real root and it is not rational.