How to graph a rational function with a hole

The video tutorial covers the process of factoring trinomials and identifying discontinuities in functions, specifically focusing on holes and asymptotes. It explains how to graph functions with holes, determine the domain and range, and explore limits and continuity at points of discontinuity. The tutorial emphasizes understanding the difference between holes and vertical asymptotes and how these affect the graph of a function.

What happens to a discontinuity when it divides out in a function?

• It becomes a vertical asymptote.

• It becomes a hole.

• It remains a discontinuity.

• It disappears completely.

Where is the hole located in the graph of the function discussed?

• At x = -3

• At x = 1

• At x = 3

• At x = 0

What is the y-coordinate of the hole in the function?

• -3

• -1

• -4

• 0

What is the domain of the function, considering the hole?

• All real numbers

• All real numbers except x = 0

• All real numbers except x = -3

• All real numbers except x = 1

What is the range of the function, considering the hole?

• All real numbers except y = 0

• All real numbers except y = 1

• All real numbers

• All real numbers except y = -4

As x approaches infinity, what does the function approach?

• A vertical asymptote

• Zero

• Infinity

• A horizontal asymptote

What is the limit of the function as x approaches -3?

• It is 3.

• It is undefined.

• It is 0.

• It is -4.