Exploring Transformations of Rational Functions

This video tutorial covers transformations on reciprocal functions, starting with an introduction to the parent function f(x) = 1/x. It explains how to analyze graphs for vertical and horizontal asymptotes and describes the effects of transformations such as horizontal and vertical shifts, reflections, and stretches. The tutorial concludes with examples to illustrate these transformations.

What is the parent function of a reciprocal function?

• f(x) = 1/x^2

• f(x) = x^2

• f(x) = 1/x

• f(x) = x

What are the horizontal and vertical asymptotes of the parent function f(x) = 1/x?

• x = 0 and y = 0

• x = 1 and y = 0

• x = 0 and y = 1

• x = 1 and y = 1

In the context of transformations, what does 'h' represent?

• Stretch/Compression

• Vertical shift

• Reflection

• Horizontal shift

What effect does a negative 'a' value have on the graph of a function?

• Stretch/Compression

• Reflection across the x-axis

• Vertical shift

• Horizontal shift

If a function is transformed with a 'k' value of -5, what is the transformation?

• Shift down 5 units

• Shift up 5 units

• Shift right 5 units

• Shift left 5 units

What does a vertical stretch factor of 2 indicate about the transformation?

• The graph is stretched vertically by a factor of 2

• The graph is stretched horizontally by a factor of 2

• The graph is compressed horizontally by a factor of 2

• The graph is compressed vertically by a factor of 2

For the function f(x) = 1/(x + 3), what is the horizontal shift?

• 3 units down

• 3 units up

• 3 units left

• 3 units right

What is the new vertical asymptote after applying the transformation x -> x + 3?

• x = 0

• x = 3

• x = -3

• x = 1

After a transformation, if the horizontal asymptote is y = -5, what was the 'k' value used?

• 1

• 0

• -5

• 5

What is the domain of a transformed reciprocal function that has a vertical asymptote at x = -3?

• (-∞, 0) U (0, ∞)

• (-∞, 3) U (3, ∞)

• (-∞, -3) U (-3, ∞)

• (-∞, ∞)