Asymptotes and intercepts of the reciprocal function

The video tutorial explains how to analyze and transform the function y = 2 / (X - 2) + 1. It covers identifying vertical and horizontal asymptotes, graph transformations, and solving for X and Y intercepts. The tutorial emphasizes understanding the parent function and applying transformations to determine new asymptotes and intercepts. Detailed steps are provided for solving equations to find intercepts, highlighting the importance of isolating variables and using the distributive property.

What transformation occurs when a function is shifted two units to the right?

• The graph moves two units down.

• The graph moves two units up.

• The graph moves two units to the left.

• The graph moves two units to the right.

What is the new vertical asymptote of the function y = 2 / (X - 2) + 1?

• X = 0

• X = 1

• X = 2

• X = -2

How does the horizontal asymptote change after the graph is shifted up by one unit?

• It remains at y = 0.

• It shifts to y = 1.

• It shifts to y = -1.

• It shifts to y = 2.

What is the X-intercept of the function y = 2 / (X - 2) + 1?

• X = 0

• X = 1

• X = 2

• X = -1

What is the Y-intercept of the function y = 2 / (X - 2) + 1?

• Y = 2

• Y = 0

• Y = 1

• Y = -1