Graphing Square Root Functions

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• Domain: {All real numbers} Range:  {All real numbers}

What is the transformation of this function compared to the parent function?

• Shifted down 2

• Shifted up 2

• Shifted left 2

• Shifted right 2

What is the equation of the graph?

What is the equation of the graph?

Identify the Range

• (- ∞, -2 ]

• [ -2, ∞ )

• (-∞, 0)

• [ 0, ∞)

What are the transformations for the graph of
the parent function f(x) = √x  to the function above 

• Vertical Stretch by a factor of 2; translated down 5 units 

• Shifted right 2 units and down 5 units 

• Vertical stretch by a factor of 2; translated up 5 units

• Vertical stretch by a factor of 2; translated right one unit 

Find the domain and range of the function
Hint:  Use a scratch graph to help you visualize things. 

• Domain: (-∞, ∞)  Range: [-∞, 4]
• Domain: [1, ∞)  Range: (-∞, 4]
• Domain: [-1. ∞) Range: [4, ∞) 
• Domain: [4, ∞) Range: [-1,∞) 

• left 1 unit, down 2 units, vertical stretch by 3

• left 1 unit, up 2 units, vertical stretch by 3

• left 1 unit, up 2 units, vertical stretch by 1/3

• right 1 unit, up 2 units