Graphing square root and cube root equations

Graphing square root and cube root equations

What order for transformations?

• Follow your order of operations

• First inside parenthesis or radicals - follow order of operations in here too!

• Second multiplication or division outside parenthesis or radicals

• Third addition or subtraction outside parenthesis or radicals

Parent function

 $f\left(x\right)=\sqrt{x}$  

• Use these three points:

• (0,0)

• (1,1)

• (4,2)

Graph

 $f\left(x\right)=-\sqrt{x}+6$  

• Transformations in order: 

• 1.  reflect over x-axis  $\rightarrow$  multiply all y by (-1)

• 2.  shift up 6 $\rightarrow$  add 6 to all the y coordinates

• For all points (x,y) in the parent function it is now (x, -y + 6)

• Parent function points (0,0), (1, 1), (4,2)

• New points: (0, 6), (1, 5), (4, 4)

 $f\left(x\right)\ =\ -\sqrt{x}+6$  

• (0,6), (1,5), (4, 4)

Multiple Choice

 $f\left(x\right)=4\sqrt{x-2}-6$  What is the first transformation?

• vertical stretch: 4y

• shift right 2: x + 2

• shift down 6:  y - 6

Multiple Choice

What is the SECOND transformation for

 $f\left(x\right)=4\sqrt{x-2}-6$  

• vertical stretch: multiply y(4)

• shift down 6: y - 6

Multiple Choice

 $y=4\sqrt{x-2}-6$  1st transformation:  x + 2.  2nd transformation:  4y.  3rd transformation is shift down 6:  y - 6.  Parent function points (x, y) which become what?

• (x, 4y - 6)

• (x + 2, 4y - 6)

• (x+ 2, y)

Multiple Select

Transformations: (x+2, 4y - 6)

Parent function points: (0,0), (1,1), (4,2)

What are the new points?

• (0,0)

• (2, -6)

• (3, -2)

• (6, 2)

 $f\left(x\right)=4\sqrt{x-2}-6$  

• (2,-6), (3, -2), (6,2)

Multiple Choice

For the graph

 $f\left(x\right)=-3\sqrt{-2x}+1$  What is the first transformation?

• Vertical stretch and reflect over x axis:  -3y

• horizontal compression/reflect over y axis:  $\frac{x}{-2}$  

• shift up 1: y + 1

Multiple Choice

For the graph

 $f\left(x\right)=-3\sqrt{-2x}+1$  What is the second transformation?

• Vertical stretch and reflect over x axis:  -3y

• horizontal compression/ reflect over y axis:   $\frac{x}{-2}$  

• shift up 1:   y + 1

Multiple Choice

For the graph

 $f\left(x\right)=-3\sqrt{-2x}+1$  What is the third transformation?

• Vertical stretch and reflect over x axis:  -3y

• horizontal compression/ reflect over y axis:   $\frac{x}{-2}$  

• shift up 1:   y + 1

Multiple Choice

 $y=-3\sqrt{-2x}+1$  

parent function points (0,0), (1,1), and (4,2).  The transformations are  $\left(\frac{x}{-2},-3y+1\right)$  

What are the new points? 

• (0,1),(-1/2, -2), (-2,-5)

• (0,-1), (-1/2, -4), (-2, -7) 

 $f\left(x\right)=-3\sqrt{-2x}+1$  

• (0,1),(-1/2,-2),(-2,-5)

Parent function:

 $f\left(x\right)=^3\sqrt{x}$  

• Points: (-1,-1), (0,0), (1, 1)

• Do all transformations in the same order as  $f\left(x\right)=\sqrt{x}$  

Multiple Choice

For

 $f\left(x\right)=2\ ^3\sqrt{x-4}$  , what is the first transformation?

• vertical stretch: 2y

• horizontal shift:  x + 4

Multiple Choice

For

 $f\left(x\right)=2\ ^3\sqrt{x-4}$  , what is the second transformation?

• vertical stretch: 2y

• horizontal shift:  x + 4

Multiple Choice

 $f\left(x\right)=2\ ^3\sqrt{x-4}$ parent function points: (-1,-1), (0,0), (1,1).  Transformations: (x + 4, 2y).  What would they be after the transformations?

• (3, -2), (4,0), (5, 2)

• (6, -1), (8,0), (10, 1)

• (6,-2), (8,0). (10, 2)

 $f\left(x\right)=2\ ^3\sqrt{x-4}$  

• (3,-2), (4,0), (5,2)

Multiple Choice

the parent function is shown. Which is the graph of

 $f\left(x\right)\ =\ 2\ ^3\sqrt{-x-4}$  

 $y\ =\ 2\ ^3\sqrt{-x-4}=2\ ^3\sqrt{-\left(x+4\right)}$  

• Parent function points (-1, -1), (0, 0), (1, 1)

• Transformations: (-x - 4, 2y)

• New points: (-3, -2), (-4, 0), (-5, 2)

Homework in Khan Academy:

• 1. Graphs of square and cube root functions

• 2. Transformations of functions Quiz 3