Question

the function $y = \frac{19,800}{x}$ is a rational function. what is the behavior of the function as $x$ approaches $+\infty$? $y$ approaches $+\infty$ $y$ approaches $-\infty$ $y$ approaches zero

Explanation:

Step1: Recall the limit of \( \frac{1}{x} \) as \( x \to +\infty \)

As \( x \) becomes very large (approaches \( +\infty \)), the value of \( \frac{1}{x} \) gets closer to 0. For example, if \( x = 1000 \), \( \frac{1}{x}=\frac{1}{1000}=0.001 \); if \( x = 1000000 \), \( \frac{1}{x}=0.000001 \), and so on.

Step2: Analyze the function \( y=\frac{19800}{x} \)

The function \( y = \frac{19800}{x} \) can be written as \( y = 19800\times\frac{1}{x} \). Since \( \frac{1}{x} \) approaches 0 as \( x \to +\infty \), multiplying a constant (19800) by a quantity that approaches 0 will result in the whole expression approaching 0. So as \( x \) approaches \( +\infty \), \( y=\frac{19800}{x} \) approaches 0.

Answer:

\( y \) approaches zero