Graph Transformations and Functions

The video tutorial introduces radical functions, focusing on square root functions and their transformations. It covers critical points, domain, and range, and clarifies the difference between positive and negative square roots. The tutorial also demonstrates graphing techniques and advanced transformations, emphasizing the importance of understanding these concepts without relying solely on calculators. The session concludes with general questions and examples to deepen understanding.

What is the simplest form of a radical function discussed in the introduction?

• y = x³

• y = √x

• y = x²

• y = 1/x

Which of the following is an imaginary number?

• √1

• √-1

• √0

• √4

When solving x² = 4, what are the possible values of x?

• -2

• 0

• 2

• ±2

Why is the domain of y = √x not all real numbers?

• Because √x is always positive

• Because √x is undefined for negative x

• Because √x is always negative

• Because √x is zero for all x

What is the difference between the graphs of y = √x and x = y²?

• Both have two branches

• Both have one branch

• x = y² has two branches

• y = √x has two branches

Why is factoring important in transformations?

• To change the function type

• To simplify calculations

• To make graphs look better

• To avoid errors in transformations

What happens to a graph when it is horizontally translated?

• It becomes wider

• It moves left or right

• It moves down

• It moves up

If a is positive and b is negative, in which quadrant does the graph lie?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV