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).
