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
- For each graph below, state whether it represents a function. Graph 1 24y Graph 2 Graph 3 4 2 -8 -6 -4 -2 -2 2 4 6 Function? ○ Yes ○ No ○ Yes ○ No Graph 4 Graph 5 8 Function? Yes No Yes No -2. ○ Yes ○ No Graph 6 4 + 2 4 -8 -6 -4 -2 2 4 6 8 Yes -4++ Noarrow_forwardPractice k Help ises A 96 Anewer The probability that you get a sum of at least 10 is Determine the number of ways that the specified event can occur when two number cubes are rolled. 1. Getting a sum of 9 or 10 3. Getting a sum less than 5 2. Getting a sum of 6 or 7 4. Getting a sum that is odd Tell whether you would use the addition principle or the multiplication principle to determine the total number of possible outcomes for the situation described. 5. Rolling three number cubes 6. Getting a sum of 10 or 12 after rolling three number cubes A set of playing cards contains four groups of cards designated by color (black, red, yellow, and green) with cards numbered from 1 to 14 in each group. Determine the number of ways that the specified event can occur when a card is drawn from the set. 7. Drawing a 13 or 14 9. Drawing a number less than 4 8. Drawing a yellow or green card 10. Drawing a black, red, or green car The spinner is divided into equal parts. Find the specified…arrow_forwardAnswer the questionsarrow_forward
- Solve the problems on the imagearrow_forwardAsked this question and got a wrong answer previously: Third, show that v3 = (−√3, −3, 3)⊤ is an eigenvector of M3 . Also here find the correspondingeigenvalue λ3 . Just from looking at M3 and its components, can you say something about the remaining twoeigenvalues? If so, what would you say?arrow_forwardDetermine whether the inverse of f(x)=x^4+2 is a function. Then, find the inverse.arrow_forward
- The 173 acellus.com StudentFunctions inter ooks 24-25/08 R Mastery Connect ac ?ClassiD-952638111# Introduction - Surface Area of Composite Figures 3 cm 3 cm 8 cm 8 cm Find the surface area of the composite figure. 2 SA = [?] cm² 7 cm REMEMBER! Exclude areas where complex shapes touch. 7 cm 12 cm 10 cm might ©2003-2025 International Academy of Science. All Rights Reserved. Enterarrow_forwardYou are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methodsarrow_forwardPlane II is spanned by the vectors: - (2) · P² - (4) P1=2 P21 3 Subspace W is spanned by the vectors: 2 W1 - (9) · 1 W2 1 = (³)arrow_forward
- 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





