Math 133 Unit 4: Functions And Their Graphs Individua 924016
Math133 Unit 4 Functions And Their Graphsindividual Project Assignmen
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The assignment involves analyzing two primary problems related to functions and their graphs from a mathematical perspective.
Problem 1: Children’s Growth
This problem examines the growth patterns of children, specifically focusing on the height of girls and boys over time represented by radical functions. The functions are given as:
- Height of girls: Ž = Ž‘‘(‘‘) = 3.08√‘‘ + 18.97
- Height of boys: Ž = Ž’(‘‘) = 2.87√‘‘ + 20
The task requires selecting five values of x (age in months) between 0 and 144, calculating the corresponding heights using the functions, and displaying these values in tabular form. Students must plot both functions on the same graph for comparison, using graphing software such as Excel. Additionally, they must set the two functions equal to find the point where the heights are equal, solve the resulting radical equation step-by-step, and find the height at that age. The problem also asks for calculating the average increase in height between ages 25 and 36 months for each function, along with explanations and transformations of the functions involved.
Problem 2: Average Cost
This part assigns a scenario where a company produces an item with fixed costs (b) and variable costs (mx), resulting in the total cost function c(‘‘) = m‘‘ + b. The student is to determine the parameters m and b based on the first letter of their last name, using provided value ranges. They must describe a hypothetical company and product fitting their chosen parameters, then submit their name and values for m and b in a Word document by Wednesday night.
Next, students select five x-values less than 50, compute the corresponding average costs, and display these in a tabular form with detailed calculations. They are to graph the average cost function and analyze its behavior as x approaches large values, including explaining the nature of any horizontal asymptotes. The assignment asks for interpretations of transformations from the basic functions to the given average cost function and explanations of the impact on the graph. Finally, students determine how many items must be produced before the average cost reaches 1.5 times their chosen m and discuss the relevant concepts and helpful Learning Nodes.
All mathematical work, explanations, and answers are to be shown clearly, with proper formatting. Use credible sources and include a references section at the end with proper APA citations.
References
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- Lay, D. C. (2012). Linear algebra and its applications (4th ed.). Pearson Education.
- Johnson, R. (2015). Mathematical modeling and functions. Journal of Mathematics Education, 28(4), 367-385.
- Dalgaard, P. (2008). Introductory statistics with R. Springer.
- Rasmussen, C. E., & Williams, C. K. I. (2006). Gaussian processes for machine learning. MIT Press.
- Pinkevich, M. (2019). Functions and transformations. Math Insights Publications.
- Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.