Transformations of Functions and Mathematical Concepts
Transformations: g(x) = af(b(x+c))+d
Parameters and Their Effects
a
- a > 1: Vertical stretch
- 0 < a < 1: Vertical compression
- a < 0: Vertical reflection
b
- b > 1: Horizontal compression
- 0 < b < 1: Horizontal stretch
- b < 0: Horizontal reflection
c
- c > 0: Shift left
- c < 0: Shift right
d
- d > 0: Shift up
- d < 0: Shift down
Examples
g(x) = f(x-3) – 1: Horizontal shift right 3 & vertical shift down 1
h(x) = -f(x): Vertical reflection
j(x) = f(-2(x+3)) + 1: Horizontal reflection, horizontal
Read MoreExam 2 Review: Finance Concepts and Calculations
Exam 2 Review
Chapter 5: Time Value of Money (Practice quizzes, MindTap, and class examples)
Key Concepts
- Future Value (FV): Represents the value of an investment at a specific future date, considering interest earned.
- Simple Interest: Interest earned only on the principal amount. FV = PV + PV(I)(N)
- Compound Interest: Interest earned on both the principal and accumulated interest. FV = PV x (1+I)^n
- Compounding: The process of converting present values into future values.
- Discounting: The process of converting
Direct Proof and Counterexample I: Introduction to Proof Techniques
Section 4.1 – Direct Proof and Counterexample I: Introduction
Discovery and Proof
Discovery and proof are integral parts of problem-solving. When you believe a statement is true, try to understand why. Success validates your discovery, while failure provides insights into the problem and may reveal the statement’s falsity.
Assumptions
- This text assumes familiarity with basic algebra laws (see Appendix A).
- We utilize the three properties of equality: For all objects A, B, and C, (1) A = A, (2) if A
Teachers’ Perceptions & Practices of Teaching Math Through Problem Solving in Senior High School
Teachers’ Perceptions & Practices of Teaching Mathematics Through Problem Solving in the Senior High School
Student Information
Student Name: Elvis Owusu
Student Number: 8110110016
Course Name: MPhil Mathematics Education
Department: Mathematics
Supervisor: Dr. M.J. Nabie
Chapter 1: Introduction
Overview
This chapter provides context for the study, outlining the background, problem statement, purpose, significance, research questions, delimitations, and limitations.
Background of the Study
Mathematics
Read MoreManufacturing and Sales Decisions with Limited Resources
HO # 7 – Manufacturing of Two Products with Limited Resources
Objective
(1) Objective Criterion: Maximize profit subject to constraining factors.
(2) Find the binding constraint (technological) given the market/demand constraint.
Resource Availability and Requirements
Hours Available:
- DLHRS: 10,000
- MHRS: 14,000
Hours Required to Produce:
- 24,000 units of Product A: 8,000 DLHRS, 12,000 MHRS
- 6,000 units of Product B: 6,000 DLHRS, 2,000 MHRS
Total Hours Required for 24,000 A & 6,000 B:
- DLHRS: 14,000
- MHRS: 14,
Statistics Final Exam Study Guide: Key Concepts & Formulas
Final Exam Study Guide
Histograms
Appropriate for quantitative data
- X-axis is quantitative
- Y-axis is the frequency of the data in the bin
- Bins are a range of values for collecting data, should be the same size
Shape
- Symmetric/Bell-shaped
- Normal
- Skewed
- Uniform
Center
- Mean – useful when data are symmetric
- Median – useful when data are skewed/outliers
- Mode – useful for categorical data
- Unimodal
- Bimodal
Spread
- Range – easy to calculate, not useful
- Interquartile range – easy to calculate, useful when data are skewed/outliers
- Standard