Graphing Reciprocals of Quadratic Functions

The video tutorial explains how to graph reciprocal functions by first sketching the denominator function, whether quadratic or linear. It covers the process of identifying zeros, understanding the behavior of reciprocal functions, and analyzing special cases with different numbers of zeros. The tutorial also discusses the domain, range, and asymptotes of these functions, providing a comprehensive guide to understanding and sketching reciprocal functions.

Why is it helpful to sketch the denominator function when graphing reciprocal functions?

• It is required by graphing rules.

• It helps in understanding the behavior of the reciprocal function.

• It makes the graph easier to erase.

• It makes the graph look more colorful.

What is the first step in graphing the function y = 1 / (x^2 - 2x - 3)?

• Graphing the reciprocal function directly.

• Identifying the zeros of the quadratic function.

• Finding the vertex of the quadratic function.

• Sketching the quadratic function.

What happens to the reciprocal function at the zeros of the quadratic function?

• It becomes zero.

• It has a vertical asymptote.

• It becomes a horizontal line.

• It intersects the x-axis.

How many branches does the reciprocal function have when the quadratic function has two zeros?

• Three

• Two

• One

• Four

What is the y-value of the vertex for the quadratic function x^2 - 2x - 3?

• 1

• 3

• -4

• 0

What is the range of the reciprocal function y = 1 / (x^2 - 2x - 3)?

• All y-values except 0

• All y-values greater than 0

• All y-values less than or equal to -1/4 and greater than 0

• All y-values less than or equal to 1/4 and greater than 0

What is the domain of the reciprocal function y = 1 / (-x^2 - 2)?

• All x-values except 2

• All real numbers

• All x-values except 0

• All x-values except -2

What is the range of the reciprocal function y = 1 / (-x^2 - 2)?

• All y-values greater than 0

• All y-values less than 0

• All y-values between -1/2 and 0

• All y-values between -1 and 0

What is the behavior of the reciprocal function when the quadratic function has a single zero?

• It has no horizontal asymptote.

• It has one vertical asymptote.

• It has two vertical asymptotes.

• It has no vertical asymptote.

What is the range of the reciprocal function y = 1 / (x^2 - 6x + 9)?

• All y-values greater than 1

• All y-values except 0

• All y-values less than 0

• All y-values greater than 0