Learning to write the domain of a rational function with an asymptotes and hole

The video tutorial explains how to identify discontinuities in functions by examining where the denominator equals zero. It distinguishes between holes and asymptotes, explaining that holes can be factored out while asymptotes cannot. The process involves factoring both the numerator and denominator to determine the type of discontinuity. The tutorial concludes by defining the domain of the function, excluding the points of discontinuity.

What is the implied domain of a function in terms of discontinuities?

• All real numbers except where the numerator is zero

• All positive numbers

• All integers

• All real numbers except where the denominator is zero

How can you identify a hole in the graph of a function?

• By factoring out common terms in the numerator and denominator

• By setting the numerator equal to zero

• By checking where the graph is undefined

• By finding where the graph crosses the x-axis

What distinguishes an asymptote from a hole in a graph?

• A hole is where the graph crosses the y-axis

• A hole can be factored out

• An asymptote can be factored out

• An asymptote is where the numerator is zero

Which of the following is true about removable discontinuities?

• They occur where the numerator is zero

• They do not affect the domain

• They can be factored out of the function

• They are always vertical asymptotes

What is the domain of the function discussed in the video?

• From negative infinity to -1, union -1 to 1, union 1 to infinity

• From -1 to 1

• All real numbers

• From negative infinity to positive infinity