Transformations of Square Root Functions

The video tutorial covers graphing square root functions, starting with the parent function and its domain, range, and key points. It explains transformations such as vertical dilation, horizontal translation, and reflection. Several examples demonstrate these transformations, showing how they affect the graph's shape and position. The tutorial concludes with complex transformations involving multiple changes.

What is the main focus of today's lesson?

• Graphing cubic functions

• Graphing linear functions

• Graphing square root functions

• Graphing exponential functions

What is the domain of the square root parent function?

• 0 to 10

• Negative infinity to 0

• 0 to positive infinity

• Negative infinity to positive infinity

Which transformation is indicated by a negative sign in front of the square root?

• Vertical stretch

• Horizontal translation

• Reflection across the x-axis

• Vertical translation

In the function f(x) = √(x - 4), what is the horizontal translation?

• 4 units up

• No translation

• 4 units right

• 4 units left

For the function f(x) = √(x + 5), what is the new domain?

• 5 to infinity

• 0 to infinity

• Negative 5 to infinity

• Negative infinity to 5

What effect does the '2' have in the function f(x) = 2√x?

• Horizontal stretch

• Horizontal compression

• Vertical stretch by a factor of 2

• Vertical compression

In the function f(x) = -√(x - 2), what is the effect of the negative sign?

• Reflection across the x-axis

• Vertical translation

• Vertical stretch

• Horizontal translation

For the function f(x) = -√(x + 1) + 6, what is the vertical translation?

• 1 unit down

• 6 units up

• 1 unit up

• 6 units down

In the function f(x) = 3√(x + 3) - 5, what is the horizontal translation?

• 5 units down

• 3 units right

• 5 units up

• 3 units left