Question

question #8
determine the range of the rational function.
(-∞,∞)
(-∞,-5.9)∪(-0.1,∞)
(-∞,-0.5)∪(2.5,∞)
(-∞,1)∪(1,∞)

Explanation:

Step1: Identify horizontal asymptote

The range of a rational - function can be determined by looking at its horizontal asymptote and the behavior of the graph. From the graph, we can see that the function has a horizontal asymptote at $y = 1$.

Step2: Analyze the graph's behavior

The graph approaches $y = 1$ but never reaches it. The function values are either less than 1 or greater than 1.

Answer:

$(-\infty,1)\cup(1,\infty)$