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Algebra Level 4

f(x)=2x2+3x2x23x4×(x4)2(x24)(x3)×x2x2x4÷2x2xx23xf(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)y=f(x) will intersect with the graph y=xy=x at the point (1,1)(1,1).

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

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

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

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