Graphing Square Root and Cube Root Functions

Which function matches the graph?

• $f\left(x\right)=\sqrt{x-4}-2$

• $f\left(x\right)=\sqrt{x+2}-4$

• $f\left(x\right)=\sqrt{x-2}-4$

• $f\left(x\right)=\sqrt{x+4}-2$

Which function matches the graph?

• $g\left(x\right)=\sqrt{x-1}+3$

• $g\left(x\right)=-\sqrt{x+1}+3$
  

• $g\left(x\right)=\sqrt{-x-1}+3$

• $g\left(x\right)=-\sqrt{x+3}-1$

Which function matches the graph?

• $f\left(x\right)=^3\sqrt{x+3}+2$

• $f\left(x\right)=-^3\sqrt{x-3}+2$

• $f\left(x\right)=^3\sqrt{x-3}+2$

• $f\left(x\right)=^3\sqrt{x-2}+3$

What are the transformations of this functions compared to the parent function?

 $f\left(x\right)=^3\sqrt{-x+2}$  

• Reflection in x

  Left 2

• Reflection in y

  Right 2
  
  

• Reflection in y
  Left 2

• Reflection in x

  Up 2
  
  

What is the equation of the graph?

• $y=-\sqrt{x+3}$

• $y=-\sqrt{x}+3$

• $y=\sqrt{-x}-3$
  

• $y=\sqrt{-x}+3$
  

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,∞)