Which parent function graphs have asymptotes?

Question

The graph of some parent functions have boundary lines called "asymptotes."

Answer 1

Rational functions - ratios of two polynomials - have asymptotes. The asymptotes can be vertical, horizontal, or slanted. Hyperbolas also have asymptotes (slanted).

Answer 2

By definition, an asymptote occurs when either the x or y values of a function approach an arbitrary value but never actually reach it. In parent functions the asymptote will typically occur at x=0 or y=0. This happens with exponential, logarithmic, or reciprocal functions. It also occurs multiple times for the tangent function. A good clue to look for is a function that contains an exponent (logarithm) or a divisor that could potentially have a value of 0.

There is a good discussion of parent functions at https://www.storyofmathematics.com/parent-functions.