A
To compare : To compare the two graphs and the transformation used.
A linear function from A to B is ALWAYS an ONTO function.
Where B equals all real numbers
Given information : The two equation of graphs are
Concept used : Graph transformation is the process of modifying an existing graph or graphed equation to produce a variation of the following graph.
Calculation:
The graph for equation
The graph for equation
B
To determine : The effect of function on polynomial function and for each set B.
A quadratic function from A to B is NEVER an ONTO function.
Where B equals all real numbers
Given information : The polynomial function is quadratic and set B are all real number.
Concept used : A function is called onto if it pairs every element in B with at least one element in A.
Calculation:
A quadratic polynomial function is of the form
The End behaviour is UP and UP , If
The End behaviour is DOWN and DOWN , If
A quadratic Function is a polynomial of even degree; therefore, it must have odd number of turning points.
Also, it is having degree 2, therefore, it can have at most
Therefore, a quadratic function will always have one turning point.
In both cases
Hence a quadratic function is NEVER an ONTO function from A to B where B= all real numbers
Example:
C
To determine : To determine the effect of function on polynomial function and for each set B.
A quadratic function from A to B is SOMETIMES an ONTO function.
Where B equals all real numbers greater than or equal to 4.
Given information : The polynomial function is quadratic and set B are all real number greater than or equal to 4.
Concept used : A function is called onto if it pairs every element in B with at least one element in A.
Calculation:
A quadratic polynomial function is of the form
The End behaviour is UP and UP , If
The End behaviour is DOWN and DOWN , If
A quadratic Function is a polynomial of even degree; therefore, it must have odd number of turning points.
Also, it is having degree 2, therefore, it can have at most
Therefore, a quadratic function will always have one turning point.
Therefore, when
Therefore, when
Hence a quadratic function is SOMETIMES an ONTO function from A to B where B= all real numbers greater than or equal to 4.
Example:
D
To determine : To determine the effect of function on polynomial function and for each set B.
A cubic function from A to B is ALWAYS an ONTO function.
Where B equals all real numbers
Given information : The polynomial function is cubic and set B are all real number.
Concept used : A function is called onto if it pairs every element in B with at least one element in A.
Calculation:
A cubic polynomial function is of the form
The End behaviour is DOWN and UP , If
The End behaviour is UP and DOWN , If
In both cases
Therefore,
Hence a cubic function is ALWAYS an ONTO function from A to B where B= all real numbers
Example:
Chapter 5 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education