square roots and cubic functions n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Square Roots and Cubic functions PowerPoint Presentation
Download Presentation
Square Roots and Cubic functions

Loading in 2 Seconds...

play fullscreen
1 / 23

Square Roots and Cubic functions - PowerPoint PPT Presentation


  • 75 Views
  • Uploaded on

Square Roots and Cubic functions. Learning Targets. Recognize and describe the following functions: Square Roots Cubics Learn about the locater points for each function and use it to determine transformations, reflections and translations. Square Roots.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Square Roots and Cubic functions' - lavender


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
learning targets
Learning Targets
  • Recognize and describe the following functions:
    • Square Roots
    • Cubics
  • Learn about the locater points for each function and use it to determine transformations, reflections and translations
square roots
Square Roots
  • The Parent Function of the square root function is:
square roots1
Square Roots

Question to pause and ponder:

Why does this graph only go one direction? What does it tell us?

square roots2
Square Roots

We cannot have negative inputs within a square root.

Try and calculate it on your graphing calculator…

Why can’t there be any negatives inputs within a square root?

?

?

square roots3
Square Roots

But can’t we have negative outputs?

A function has to pass the vertical line test, this means that every function must have exactly one output for every input.

Therefore since this is a function our range is limited.

?

square roots4
Square Roots
  • Characteristics:
  • Asymmetrical
  • Restricted domain and range
transformations
Transformations

Lets think about how we can transform, translate or reflect this function?

Can we vertically or horizontally translate ?

Can we reflect over the x axis?

Can we stretch or compress this function?

standard equation for
Standard Equation for

Vertical Translation

Reflects over x-axis when negative

Vertical Stretch or Compress

Stretch:

Compress:

Horizontal Translation

(opposite direction)

locater point
Locater Point

This is a point on the graph that is used to compare two functions and determine the differences between them.

For the Square root function we will use the origin, (0,0), of the parent function.

example 1
Example #1

How was this function transformed?

Vertical Translation: -2

Horizontal Translation:+3

example 2
Example #2

How was this function transformed?

Vertical Translation: +3

Reflected over the x-axis

example 3
Example #3

How was this function transformed?

Vertical Compression

cubics
Cubics
  • The Parent Function of the cubic function is:
cubics1
Cubics
  • Characteristics:
  • Asymmetrical
  • No maximum/minimum
  • Domain and Range is all real numbers
transformations1
Transformations

Lets think about how we can transform, translate or reflect this function?

Can we vertically or horizontally translate ?

Can we reflect over the x axis?

Can we stretch or compress this function?

standard equation for1
Standard Equation for

Vertical Translation

Reflects over x-axis when negative

Vertical Stretch or Compress

Stretch:

Compress:

Horizontal Translation

(opposite direction)

*Are you starting to see a pattern

with these function transformations?

locater point1
Locater Point

For the cubic function we will use the origin, (0,0), of the parent function.

example 11
Example #1

How was this function transformed?

Vertical Translation: -4

Horizontal Translation:-4

example 21
Example #2

How was this function transformed?

Horizontal Translation: +1

Reflected over the x-axis

example 31
Example #3

How was this function transformed?

Stretch Factor of 3

determine the transformations
Determine the Transformations

+5

  • Helpful Tips:
  • Determine the function family
  • Plot the parent graph
  • Determine the locater point
  • Compare the transformed graph with the parent graph
homework
Homework

Worksheet #5