Graphing Radical Functions

5.3: Graphing Radical Functions

Algebra II, Honors

Recall Transformation rules!

• a plus or minus OUT of the root, is up or down

• a plus or minus Inside the root is left (+) or right (-1)

• The a in the front is the scale

• if a is negative, our graph flips upside down

Multiple Choice

Describe the transformation taking place in the given function

 $f\left(x\right)=3\sqrt{x-2}+5$  

• a stretch by a factor of 3
  Shift right 2
  Shift up 5

• a stretch by a factor of 3
  Shift up 2
  Shift right 5

• a shrink by a factor of 3
  Shift down 2
  Shift left 5

• A shrink bay  factor of 3

  Shift right 2
  Shift down 5

Multiple Select

Check off all transformations taking place in the following function. $f\left(x\right)=^3\sqrt{x-9}+3$  

• Shifting Up 9

• Shifting down 3

• Shifting right 9

• Shifting left 9

• Shifting up 3

Multiple Select

Check the transformation taking place.$f\left(x\right)=-4\ \ ^3\sqrt{-x+7}-9$  

• Flip over the x-axis

• Flip over the y-axis

• Stretch by a factor of 4

• Shrink by a factor of 4

Multiple Select

Check the transformation taking place.$f\left(x\right)=-4\ \ ^3\sqrt{-x+7}-9$  

• Shift right 7

• Shift left 7

• Shift up 9

• Shift down 9

Parent Function: Square root

• The x has to be positive or we end up in the imaginary plane.

• The y will always be positive as you can't pull a negative out from inside the square root.

Multiple Choice

Which graph shows the following function?

 $f\left(x\right)=\sqrt{x-9}+3$  

Multiple Choice

Which graph shows the following function?

 $f\left(x\right)=\sqrt{-x}+5$  

Multiple Choice

What is the "vertex" (endpoint) of the following function?

 $f\left(x\right)=-3\sqrt{x+6}-3$  

• (6, 3)

• (-6, 3)

• (-6, -3)

• (3, -3)

Multiple Choice

What is the "vertex" (endpoint) of the following function?

 $f\left(x\right)=\sqrt{-x-2}-7$  

• (2, -7)

• (-2, 7)

• (7, 2)

• (-7, -2)

Parent Function: Cube root

• Notice how it has a turning point, not an endpoint

• Because a cubed root can be a negative the domain and range are Both all real numbers.

• It has all the same transformation rules.

Multiple Choice

Which graph shows the following function?

 $f\left(x\right)=-2\ \ ^3\sqrt{x-9}$  

Multiple Choice

What is the turning point of the following function?

 $f\left(x\right)=\ \ ^3\sqrt{x-6}+5$  

• (6, 5)

• (-6, 5)

• (-6, -5)

• (6, -5)

Multiple Choice

 What is the turning point of the following function?$f\left(x\right)=-\frac{3}{4}\ \ ^3\sqrt{x+5}-4$  

• (5, 4)

• (-5, -4)

• (-5, 4)

• (5, -4)

Multiple Choice

Which graph shows the following function?

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

Graphing Parabola

• Notice how it's NOT a function

• The domain is still limited to positive numbers

• Because in order to solve, we made the root it has a + and - possibility