The end behavior of [tex]f(x) = \frac{3\cdot x - 4}{x + 6}[/tex] is 3.
The end behavior of a rational function is the value of the horizontal asymptote to which the function tends when [tex]x[/tex] tends to [tex]\pm \infty[/tex]. We can determine the end behavior as following:
[tex]f(x) = 3 - \frac{22}{x+6}[/tex]
When [tex]x[/tex] tends to [tex]\pm \infty[/tex], then [tex]\frac{22}{x+6} \to 0[/tex]. Hence, we conclude that the end behavior of [tex]f(x) = \frac{3\cdot x - 4}{x + 6}[/tex] is 3.
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