Transformations and Properties of Functions

The video tutorial covers transforming rational functions, focusing on domain, range, and asymptotes. It explains synthetic division and how to apply transformations to rational functions, including reflections, vertical stretches, and translations. The tutorial provides examples and step-by-step guidance to help understand the concepts.

What is the main focus of the video tutorial?

• Solving quadratic equations

• Transforming rational functions

• Graphing linear functions

• Understanding logarithms

What is the domain restriction mentioned in the video?

• X cannot equal 2

• X cannot equal -4

• X cannot equal 0

• X cannot equal 4

How can the domain be expressed in interval notation?

• (-∞, 4) ∪ (4, 4)

• (-∞, -4) ∪ (-4, ∞)

• (-∞, 4) ∪ (4, ∞)

• (-∞, -4) ∪ (4, ∞)

What is the range of the function with an asymptote at y = 2?

• (-∞, 1) ∪ (1, ∞)

• (-∞, 2) ∪ (2, ∞)

• (-∞, 0) ∪ (0, ∞)

• (-∞, 3) ∪ (3, ∞)

What mathematical process is used to rewrite the function in a specific form?

• Long division

• Completing the square

• Partial fraction decomposition

• Synthetic division

What is the first transformation applied to the rational function?

• Vertical stretch

• Horizontal shift

• Reflection over the x-axis

• Translation up

What is the vertical stretch factor mentioned in the transformations?

• 5

• 3

• 11

• 2

In which quadrants does the function appear after reflection?

• Quadrants 3 and 4

• Quadrants 1 and 2

• Quadrants 2 and 4

• Quadrants 1 and 3

What is the final vertical translation applied to the function?

• Down 5

• Up 5

• Down 2

• Up 2

What is the new x-asymptote after the transformations?

• x = 0

• x = -4

• x = 1

• x = -1