Respuesta :

The given expression is:

[tex]f(x)= \frac{x-1}{ x^{2} -x-6} \\ \\ f(x)= \frac{x-1}{ x^{2} -3x+2x-6} \\ \\ f(x)= \frac{x-1}{x(x-3)+2(x-3)} \\ \\ f(x)= \frac{x-1}{(x-2)(x+3)} [/tex]

The above expression shows that the vertical asymptote of f(x) are x = 2 and x = -3. This means, at x = 2 and x = -3 f(x) approached infinity.

The zero of f(x) is x = 1. This means f(x) crosses x-axis at x = 1. Replacing x by , we get f(0) = 1/6 .

If we observe the graphs, only the first graph satisfies all these conditions. Therefore, first graph is the graph of f(x). 

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