Answer
$f(0) = 3$
$\lim\limits_{x \to 0^-}f(x) = 4$
$\lim\limits_{x \to 0+}f(x) = 2$
$\lim\limits_{x \to 4^-}f(x) = -\infty$
$\lim\limits_{x \to 4^+}f(x) = \infty$
$\lim\limits_{x \to -\infty} f(x) = -\infty$
$\lim\limits_{x \to \infty} = 3$
Work Step by Step
$f(0) = 3$
$\lim\limits_{x \to 0^-}f(x) = 4$
As $x$ approaches $0$ from the left, the value of the function gets closer and closer to 4
$\lim\limits_{x \to 0+}f(x) = 2$
As $x$ approaches $0$ from the right, the value of the function gets closer and closer to 2
$\lim\limits_{x \to 4^-}f(x) = -\infty$
As $x$ approaches $4$ from the left, the value of the function becomes larger magnitude negative numbers.
$\lim\limits_{x \to 4^+}f(x) = \infty$
As $x$ approaches $4$ from the right, the value of the function becomes larger magnitude positive numbers.
$\lim\limits_{x \to -\infty} f(x) = -\infty$
As $x$ approaches larger magnitude negative numbers, the value of the function becomes larger magnitude negative numbers
$\lim\limits_{x \to \infty} = 3$
As $x$ approaches larger magnitude positive numbers, the value of the function gets closer and closer to 3
