Square Roots and Cubic functions

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# Square Roots and Cubic functions - PowerPoint PPT Presentation

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.

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### 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
• The Parent Function of the square root function is:
Square Roots

Question to pause and ponder:

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

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 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 Roots
• Characteristics:
• Asymmetrical
• Restricted domain and range
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

Vertical Translation

Reflects over x-axis when negative

Vertical Stretch or Compress

Stretch:

Compress:

Horizontal Translation

(opposite direction)

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

Vertical Translation: -2

Horizontal Translation:+3

Example #2

Vertical Translation: +3

Reflected over the x-axis

Example #3

Vertical Compression

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

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 Point

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

Example #1

Vertical Translation: -4

Horizontal Translation:-4

Example #2

Horizontal Translation: +1

Reflected over the x-axis

Example #3

Stretch Factor of 3

Determine the Transformations

+5