Question

question #3 determine the range of the rational function. (-∞,-3)∪(2,∞) (-∞,-3)∪(-3,∞) (-∞,2)∪(2,∞) (-∞,∞)

Explanation:

Step1: Identify horizontal asymptote

The horizontal asymptote of the rational - function graph is at \(y = 2\). As \(x\to\pm\infty\), the function approaches \(y = 2\), but never reaches it.

Step2: Analyze the range

The range of a function is the set of all possible \(y\) - values. Since the function can take on any value except \(y = 2\), the range is all real numbers except \(y = 2\), which is written in interval notation as \((-\infty,2)\cup(2,\infty)\).

Answer:

\((-\infty,2)\cup(2,\infty)\)