Square Roots and Cubics

Square Roots and Cubic functionsLearning TargetsRecognize and describe the following functions:Square RootsCubicsLearn about the locater points for each function and use it to determine transformations, reflections and translationsSquare Roots

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 cant there be any negatives inputs within a square root???Square Roots

But cant 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:

AsymmetricalRestricted domain and rangeTransformationsLets think about how we can transform, translate or reflect this function?Reflects over x-axis when negativeHorizontal Translation(opposite direction)Vertical TranslationLocater PointThis 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

How was this function transformed?Vertical Translation: -2Horizontal Translation:+3Example #2

How was this function transformed?Vertical Translation: +3Reflected over the x-axisExample #3

How was this function transformed?Vertical CompressionCubics

Cubics

Characteristics:

AsymmetricalNo maximum/minimumDomain and Range is all real numbersTransformationsLets think about how we can transform, translate or reflect this function?Reflects over x-axis when negativeHorizontal Translation(opposite direction)Vertical Translation*Are you starting to see a patternwith these function transformations?Locater PointFor the cubic function we will use the origin, (0,0), of the parent function.

Example #1

How was this function transformed?Vertical Translation: -4Horizontal Translation:-4Example #2

How was this function transformed?Horizontal Translation: +1Reflected over the x-axisExample #3

How was this function transformed?Stretch Factor of 3Determine the TransformationsHelpful Tips:Determine the function familyPlot the parent graphDetermine the locater pointCompare the transformed graph with the parent graphHomeworkWorksheet #5