Question

6.7.3 quiz: writing rational functions
question 5 of 10
according to the graph of ( h(w) ) below, the ( w )-axis is also the ______ for ( h(w) ).

Explanation:

Step1: Recall the definition of a horizontal asymptote

A horizontal asymptote of a function \(y = f(x)\) (in this case \(H(w)\)) is a horizontal line \(y = k\) that the graph of the function approaches as \(x\to\pm\infty\) (or \(w\to\pm\infty\) here).

Step2: Analyze the behavior of \(H(w)\) as \(w\to\infty\)

Looking at the graph of \(H(w)\), as \(w\) gets larger and larger (i.e., as \(w\to\infty\)), the values of \(H(w)\) get closer and closer to \(0\). The equation of the \(w -\)axis is \(H(w)=0\).

Answer:

horizontal asymptote