Question

part a. draw the horizontal asymptote. include the equation for this asymptote.
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Explanation:

Step1: Recall Horizontal Asymptote Rule

For rational functions or exponential/logarithmic functions, horizontal asymptotes are determined by the end - behavior as \(x\to\pm\infty\). From the graph, as \(x\) approaches positive or negative infinity, we observe the \(y\) - value that the graph approaches. Looking at the graph, the lower part of the graph (the right - hand curve) and the left - hand curve seem to approach \(y = 0\) as \(x\) goes to positive and negative infinity respectively.

Step2: Determine the Equation

The horizontal asymptote is a horizontal line, and its equation is of the form \(y = k\), where \(k\) is the \(y\) - value that the function approaches as \(x\to\pm\infty\). Since the graph approaches \(y = 0\) as \(x\) goes to \(\pm\infty\), the equation of the horizontal asymptote is \(y=0\). To draw it, we draw a horizontal line passing through \(y = 0\) (the \(x\) - axis) across the coordinate plane.

Answer:

The equation of the horizontal asymptote is \(y = 0\). To draw it, draw a horizontal line along the \(x\) - axis (since \(y = 0\) is the \(x\) - axis) on the given coordinate plane.