Transformations and Properties of Reciprocal Functions

This video tutorial explores the reciprocal function family, focusing on their general form and graphing techniques. It covers how to graph reciprocal functions, compare different graphs, and apply transformations such as vertical stretches and shifts. The tutorial also explains how to identify and use asymptotes in graphing, providing a comprehensive understanding of reciprocal functions and their transformations.

What is the general form of a reciprocal function?

• a/(x + h) - k

• ax + h + k

• a/x + h + k

• a/(x - h) + k

What is a vertical asymptote?

• A line where the graph crosses the x-axis

• A line where the graph is undefined

• A line where the graph approaches but never touches

• A line where the graph crosses the y-axis

Where does the vertical asymptote occur for the function f(x) = 2/x?

• x = -1

• x = 2

• x = 1

• x = 0

What happens to the graph of f(x) = 2/x when x = 1?

• The graph equals 1

• The graph equals 0

• The graph equals 2

• The graph is undefined

How does the graph of g(x) = 1/2x compare to f(x) = 2/x?

• It is a horizontal stretch

• It is a vertical stretch

• It is a vertical compression

• It is a horizontal compression

What is the effect of a negative 'a' value on the graph?

• The graph shifts up

• The graph reflects over the x-axis

• The graph reflects over the y-axis

• The graph shifts down

How do you find the new center of a graph with multiple changes?

• By finding the slope

• By finding the y-intercept

• By finding the x-intercept

• By finding the vertical and horizontal asymptotes

What is the transformed function of m(x) = 1/x with a vertical stretch of 2 and asymptotes at x = 1 and y = -4?

• m(x) = 2/(x + 1) + 4

• m(x) = 1/(x + 1) - 4

• m(x) = 2/(x - 1) - 4

• m(x) = 1/(x - 1) + 4