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Algebra Level 4

\[f(x)=\frac{2 x^2+3 x-2}{x^2-3 x-4}\times\frac{(x-4)^2}{(x^2-4)(x-3)}\times\frac{x^2-x-2}{x-4}\div\frac{2x^2-x}{x^2-3x}\]

Consider this expression above. Which of the following statements is correct?

A: A graph of \(y=f(x)\) will intersect with the graph \(y=x\) at the point \((1,1)\).

B: \(f(x)\) can be simplified as \(Mx+N\) where \(M\) and \(N\) are non-zero constants and \(N=1\).

C: A graph of \(y=f(x)\) has a \(y\)-intercept where \(y=1\).

D: \(f(x)\) is undefined for exactly 4 values of \(x\).


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