Graphing a reciprocal function with transformations

The video tutorial covers graphing techniques using transformations. It begins with an introduction to graphing and the importance of understanding the parent graph. The instructor explains how to apply transformations using parameters a, h, and k, and demonstrates the use of asymptotes in graphing. The tutorial includes evaluating points around asymptotes and provides a step-by-step graphing process with examples. Finally, it discusses determining new asymptotes, domain, and range for the transformed graph.

What is the first step in graphing a transformed function?

• Graph the parent function

• Shift the graph vertically

• Estimate the graph

• Use a graphing calculator

If a transformation has a = 2, h = 4, and k = 2, what does 'h' indicate?

• Shift left

• Shift right

• Horizontal compression

• Vertical stretch

How do you determine the new position of the vertical asymptote after a shift?

• By adding the value of 'k'

• By subtracting the value of 'a'

• By shifting it horizontally by 'h'

• By multiplying by 'a'

What should you evaluate to understand the effect of a stretch on the graph?

• The axis of symmetry

• Two points on either side of the asymptote

• The parent graph

• The asymptotes

What is the new vertical asymptote if the graph is shifted right by 4 units?

• x = 2

• x = 0

• x = 4

• x = -4

What is the domain of the function after transformation?

• All real numbers except y = 0

• All real numbers except x = 4

• All real numbers except x = 0

• All real numbers except y = 2

What is the range of the function after transformation?

• All real numbers except x = 2

• All real numbers except y = 0

• All real numbers except y = 4

• All real numbers except y = 2