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Math·Advanced Math·Nonlinear functions

hard

In the $xy$-plane, the graph of function $f$, where $y=f(x)$, has exactly $8$ $x$-intercepts. One of these $x$-intercepts is $(17,0)$. The rational function $g$ is defined by $g(x)=\frac{f(x)}{x-17}$. In the $xy$-plane, how many $x$-intercepts does the graph of $y=g(x)$ have?

1

7