$f$ is a polynomial function of degree 42 : The graph of $f$ has at most x-intercepts. The graph of $f$ has at most turning points.

Step 1 ：Let $f$ be a polynomial function of degree 42.

Step 2 ：The number of x-intercepts of a polynomial function is determined by the degree of the polynomial. A polynomial of degree n can have at most n x-intercepts.

Step 3 ：Thus, the graph of $f$ has at most \(\boxed{42}\) x-intercepts.

Step 4 ：The number of turning points of a polynomial function is also determined by the degree of the polynomial. A polynomial of degree n can have at most n-1 turning points.

Step 5 ：Thus, the graph of $f$ has at most \(\boxed{41}\) turning points.