Question

Given the function


`f(x) = (x + 4){(x - 2)}^(2)`
Determine the end behavior of the graph of the function. Show all/any work​

Answer 1

`lim \: f(x) = ( \infty + 4)( \infty - 2) {}^(2) \\ x - > \infty`

`lim \: f(x) = \infty * \infty \\ x - > \infty`

`lim \: f(x)= \infty \\ x - > \infty`

`lim \: (f(x))/(x) = \frac{x(1 - (4)/(x))(x - 2) {}^(2) }{x} \\ x - > \infty`

`lim \: (f(x))/(x) = (1)( \infty - 2) {}^(2) \\ x - > \infty`

`lim \: (f(x))/(x) = \infty \\ x - > \infty`

We can then say that the function f(x)=(x-4)(x-2)² admits an asymptotic direction parallel to the y-axis at +∞ and -∞ as well since we have to follow the same steps.