Graphing Square Root Functions with Transformations

This lesson covers graphing square root functions using transformations. It begins with a review of square roots and transformations, explaining rigid and non-rigid transformations. The lesson clarifies common misunderstandings about evaluating square roots, focusing on principal roots. It then demonstrates graphing square root functions using a t-table, discussing the domain and range. Finally, it applies transformations to square root functions, explaining horizontal and vertical shifts.

Why can't negative numbers have real square roots?

• Because they are not integers

• Because they are not whole numbers

• Because no number squared equals a negative number

• Because they are not rational numbers

What is the principal square root of a number?

• The negative square root

• The positive square root

• Both positive and negative square roots

• The square of the number

How is the side length of a square related to its area?

• It is half of the area

• It is the square root of the area

• It is the cube root of the area

• It is the square of the area

Why does the square root function have a stopping point?

• Because it cannot be graphed

• Because it cannot take negative x-values

• Because it has no range

• Because it is a linear function

What is the domain of the basic square root function?

• x is less than 0

• x is greater than or equal to 0

• x is less than or equal to 0

• x is greater than 0

How does subtracting a number inside the square root affect the graph?

• It shifts the graph down

• It shifts the graph up

• It shifts the graph to the right

• It shifts the graph to the left

What is the range of the function g(x) = √(x - 3) + 2?

• y is greater than or equal to 2

• y is greater than or equal to 3

• y is less than or equal to 2

• y is less than or equal to 3