a.
To determine: the function rule that models the ordered pairs of each pattern.
Pattern 1 has a function of
Pattern 2 has a function of
Given information:
Pattern 1:
Pattern 2:
Concept Used:
The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.
Calculation:
The first four pairs in pattern 1 are
Notice that the
Therefore, pattern 1 follow
The first four pairs in pattern 2 are
Notice that the
Therefore, pattern 1 follow
b.
To graph: the function
The graph is shown below:
The function
Given information:
Pattern 1 has a function of
Pattern 2 has a function of
Concept Used:
Polynomial Function: A single term or the sum of two or more terms containing variables with positive whole-number exponents. You cannot have a variable in the denominator (this means that you can't divide by
Exponential Function: This type of function has an
Calculation:
The first four pairs in pattern 1 are
The first four pairs in pattern 2 are
Using the ordered pair, plot the graph of pattern 1 and pattern 2 functions.
The graph is shown below:
From the above graph, it is observed that the function
c.
To interpret: the value of
The pattern 2 which is exponential in nature exceeds pattern 1 which is polynomial in nature.
Given information:
Pattern 1:
Pattern 2:
Concept Used:
Polynomial Function: A single term or the sum of two or more terms containing variables with positive whole-number exponents. You cannot have a variable in the denominator (this means that you can't divide by
Exponential Function: This type of function has an
Calculation:
The graph is shown below:
From the above graph, it is observed that the pattern 2 is exponential in nature exceeds pattern 1 which is polynomial in nature.
Chapter 5 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
- 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