Learn how to determine asymptotes and domain of a reciprocal function

The video tutorial explains how to identify discontinuities in a function by setting the denominator equal to zero. It discusses the concept of non-removable discontinuities, which create asymptotes rather than holes in the graph. The domain of the function is described, and the difference between holes and asymptotes is highlighted. The tutorial concludes with instructions for graphing and homework assignments.

What is the first step in identifying a discontinuity in a function?

• Set the denominator equal to zero

• Calculate the limit of the function

• Set the numerator equal to zero

• Find the derivative of the function

What type of discontinuity is created when it cannot be factored out?

• Point discontinuity

• Continuous function

• Non-removable discontinuity

• Removable discontinuity

What does a non-removable discontinuity create in a graph?

• A hole

• A peak

• A valley

• An asymptote

What is the domain of a function with a discontinuity at x = 1?

• Negative infinity to 1, union 1 to positive infinity

• Negative infinity to positive infinity

• 1 to positive infinity

• Negative infinity to 1

What is the difference between a hole and an asymptote in a graph?

• A hole is a point, an asymptote is a line

• Both are lines

• A hole is a line, an asymptote is a point

• Both are points