Exploring Graphs of Square Root Functions

The video tutorial explores the graph of y = √x, discussing its domain and how it can be transformed through vertical and horizontal shifts, as well as flipping over axes. The tutorial explains how adding constants outside or inside the radical affects the graph's position and orientation, and demonstrates these transformations with examples.

What is the domain of the function y = √x?

• x > 0

• x ≤ 0

• x ≥ 0

• x < 0

What is the value of y when x = 4 for the function y = √x?

• 3

• 4

• 2

• 1

Tags

CCSS.HSF.IF.A.2

How do you shift the graph of y = √x up by 4 units?

• y = √(x - 4)

• y = √(x) + 4

• y = √(x) - 4

• y = √(x + 4)

Tags

CCSS.HSF.BF.B.3

What happens to the graph of y = √x when you add 3 inside the radical?

• It shifts down by 3 units

• It shifts up by 3 units

• It shifts to the right by 3 units

• It shifts to the left by 3 units

Tags

CCSS.HSF.BF.B.3

What is the new function if you shift y = √x to the left by 3 units?

• y = √(x - 3)

• y = √(x) - 3

• y = √(x + 3)

• y = √(x) + 3

Tags

CCSS.HSF.BF.B.3

How do you reflect the graph of y = √x over the y-axis?

• y = √(x - 3)

• y = √(-x)

• y = √(x) + 3

• y = -√(x)

Tags

CCSS.HSF.BF.B.3

What is the domain of the function y = √(-x + 3)?

• x > -3

• x ≥ -3

• x ≤ -3

• x < -3

How do you reflect the graph of y = √(-x + 3) over the x-axis?

• y = -√(-x + 3)

• y = √(x - 3)

• y = √(-x - 3)

• y = -√(x + 3)

Tags

CCSS.HSF.BF.B.3

What is the new function if you shift y = -√(-x + 3) down by 4 units?

• y = -√(-x + 3) + 4

• y = √(-x + 3) - 4

• y = √(-x + 3) + 4

• y = -√(-x + 3) - 4

Tags

CCSS.HSF.BF.B.3

Which transformation is applied to y = √x to get y = -√(-x + 3) - 4?

• Shift down by 4 units and reflect over the x-axis

• Shift left by 3 units and reflect over the x-axis

• Shift up by 3 units and reflect over the x-axis

• Shift down by 4 units and reflect over the y-axis

Tags

CCSS.HSF.BF.B.3