Maths Paper 1, November 2024, question 9.4

The diagram below shows the graph of a cubic function $g$ with turning points P$(1;8)$ and Q$(2;7)$. The graph cuts the $y$-axis at R$(0;3)$. Determine all the values of $k$ for which $y=g(x)+k$ has exactly THREE positive $x$-intercepts.