Block 1/29-30 Graphing Square Roots

If we graph a new equation below:

 $Y\ =\ \sqrt{X\ }+\ 8$  
Relative to the parent function  $Y\ =\ \sqrt{X}$   

• The new equation will be translated 8 units to the left

• The new equation will be translated 8 units up

• The new equation will be translated 8 units down

 $f\left(x\right)\ =a\sqrt{\frac{1}{b}\left(x-h\right)}\ \ \ +\ k$  
If we use the equation above to graph a square root function, what will the variable "h" tell us?

• How far right or left the graph will move relative to the parent function

• How far up or down the graph will move relative to the parent function

• The compression or expansion of the graph relative to the parent function

 $f\left(x\right)\ =a\sqrt{\frac{1}{b}\left(x-h\right)}\ \ \ +\ k$  

In the equation above, the variable "k" will tell us:

• How far the graph moves right or left relative to the parent function.

• How far the graph moves up or down relative to the parent function.

• How much the graph is expanded or compressed relative to the parent function.

 $f\left(x\right)\ =a\sqrt{\frac{1}{b}\left(x-h\right)}\ \ \ +\ k$  

When graphing the equation above, we know that the new translated point for  (0,0) in the parent function will be:

• (x - h, k)

• (h, k)

• (0,0)

What are the transformation(s) of this function compared to the parent function?

• Shifted down 2 units

• Shifted up 2 units

• Shifted left 2 units

• Shifted right 2 units

Which of these functions shifts the parent function 3 units to the left?

Describe the transformation.

• Shifts down 1 unit

• Reflect over y-axis

• Shifts up 1 unit

• Reflect over x-axis

What function best describes this graph?

Which of these functions represents a shift 5 units to the right and down 1 unit?

What are the transformations being applied to the parent function?

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

• Shifted right 2 units and down 5 units 

• Vertical stretch by a factor of 2; shifted left 5 units

• Vertical stretch by a factor of 2; shifted right 5 unit