Question

question #1
determine the range of the rational function.
(-∞,∞)
(-∞,-2)∪(1,∞)
(-∞,-2)∪(-2,∞)
(-∞,-4)∪(2,∞)

Explanation:

Step1: Identify horizontal asymptote

The range of a rational - function is all real numbers except the $y$ - value of the horizontal asymptote (if it exists). By observing the graph, we can see that the function has a horizontal asymptote at $y = - 2$.

Step2: Determine the range

The function can take on any $y$ - value except $y=-2$. In interval notation, the range is $(-\infty,-2)\cup(-2,\infty)$.

Answer:

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