Find the domain, any asymptotes, and the - and -intercepts of . Then graph the
function.

What is the domain of ?
A.
B.
C.

The domain of is . This is because the function is undefined when , as dividing by zero is not allowed.

To identify any asymptotes, we see there’s a vertical asymptote at since the function blows up (approaches infinity) near this point. We also have a horizontal asymptote at when considering the behavior of as approaches or .

For real-world application, you might encounter this type of function in contexts where you analyze rates, such as physics or economics, where quantities change in relation to time or cost. Understanding the behavior of such functions can help model and predict real-world phenomena, like profit margins that change based on fixed costs.

If you’re graphing it, start with plotting the intercepts. The -intercept occurs when , giving . The -intercept is found by setting the numerator equal to zero; thus, leads to . Mix these crucial points with the asymptotes, and you’ll have a nicely detailed graph!