Insights By Scott Ernst

Project Autodidact

Project Details: https://insightsbyse.com/projectautodidact/

Scott Ernst Bio: https://insightsbyse.com/aboutscotternst/

Project Contact: InsightsBySE@protonmail.com

Progress Report Scope (S01-M01-D03-AllParts)

Stage 1 of 4: Review of Mathematics, Probability, and Statistics

Module 1 of 3: Foundations of Arithmetic and Algebra

Day 3 of 5: Functions and Their Properties

Parts 1 through 10: See below

Summary Of Goals Achieved

1. Reviewed rules of function notation
2. Reviewed procedures for defining a function, identifying the domain, and finding the range
3. Reviewed definition, notation, components, properties, and applicability of a linear equation, linear inequality, and linear function
4. Reviewed procedures for evaluating a linear function
5. Reviewed procedures for graphing a linear function
6. Reviewed procedures for transforming linear equations into slope-intercept form
7. Reviewed procedures for testing data points for linearity
8. Reviewed procedures for function translation (i.e., shift) (horizontal translation left, horizontal translation right, vertical translation up, and vertical translation down)
9. Reviewed procedures for function scaling (horizontal stretch, horizontal compression, vertical stretch, and vertical compression)
10. Reviewed definition, notation, terminology, components, properties, and applicability of inverse functions (existence property, injective property, composition property, domain-range interchange property, reflection property, uniqueness property, monotonicity preservation property, and inverse functions and derivatives property)
11. Reviewed procedures for finding an inverse function
12. Reviewed definition, notation, terminology, components, properties (vertex, axis of symmetry, focus, directrix, and coefficients), and features of a parabola (direction of opening, concavity, X-intercepts (roots), Y-intercept, symmetry, focal length, domain and range, and end behavior)
13. Reviewed procedures for transforming quadratic equations into vertex form
14. Reviewed definition, notation, terminology, components, properties, and applicability of a quadratic equation, quadratic inequality, and quadratic function
15. Reviewed definition, notation, terminology, components, properties, and applicability of the quadratic formula
16. Reviewed methods for solving quadratic equations (factoring, quadratic formula, completing the square, and graphing)
17. Reviewed definition, notation, terminology, components, properties, and applicability of an exponential function
18. Reviewed procedures to derive an exponential function from given data or conditions
19. Reviewed role of Euler’s number in exponential functions
20. Reviewed the use of functions in data transformations, focusing on feature scaling and normalization.  NOTE: Specific methods and procedures for data transformations will be subsequently studied
21. Reviewed the use of piecewise functions for predictive and forecasting purposes.  NOTE:Specific methods and procedures for the use of piecewise functions for predictive and forecasting purposes will be subsequently studied
22. Reviewed procedures for choosing the type of function(s) (linear, polynomial, exponential, logarithmic, logistic, power, and/or sinusoidal) for predictive and forecasting purposes
23. Reviewed methods for fitting the curve of a type of function (linear, polynomial, exponential, logarithmic, logistic, power, and/or sinusoidal) for predictive and forecasting purposes

Part 1 of 10

Goal 1 Statement: Review rules of function notation

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for defining a function, identifying the domain, and finding the range

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 2 of 10

Goal 1 Statement: Review definition, notation, components, terminology, properties, and applicability of a linear equation, linear inequality, and linear function

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for evaluating a linear function

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review procedures for graphing a linear function

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Goal 4 Statement: Review procedures for transforming linear equations into slope-intercept form

Goal 4 Plan: Read source materials

Goal 4 Work Product: None

Goal 4 Result: Completed

Goal 5 Statement: Review procedures for testing data points for linearity

Goal 5 Plan: Read source materials

Goal 5 Work Product: None

Goal 5 Result: Completed

Part 3 of 10

Goal 1 Statement: Review procedures for function translation (i.e., shift) (horizontal translation left, horizontal translation right, vertical translation up, and vertical translation down)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for function scaling (horizontal stretch, horizontal compression, vertical stretch, and vertical compression)

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 4 of 10

Goal 1 Statement: Review definition, notation, terminology, components, properties, and applicability of inverse functions (existence property, injective property, composition property, domain-range interchange property, reflection property, uniqueness property, monotonicity preservation property, and inverse functions and derivatives property)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for finding an inverse function

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 5 of 10

Goal 1 Statement: Review definition, notation, terminology, components, properties (vertex, axis of symmetry, focus, directrix, and coefficients), and features of a parabola (direction of opening, concavity, X-intercepts (roots), Y-intercept, symmetry, focal length, domain and range, and end behavior)

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures for transforming quadratic equations into vertex form

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Part 6 of 10

Goal 1 Statement: Review definition, notation, terminology, components, properties, and applicability of a quadratic equation, quadratic inequality, and quadratic function

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review definition, notation, terminology, components, properties, and applicability of the quadratic formula

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review methods for solving quadratic equations (factoring, quadratic formula, completing the square, and graphing)

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Part 7 of 10

Goal 1 Statement: Review definition, notation, terminology, components, properties, and applicability of an exponential function

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review procedures to derive an exponential function from given data or conditions

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed

Goal 3 Statement: Review role of Euler’s number in exponential functions

Goal 3 Plan: Read source materials

Goal 3 Work Product: None

Goal 3 Result: Completed

Part 8 of 10

Goal 1 Statement: Review the use of functions in data transformations, focusing on feature scaling and normalization

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

NOTE: Specific methods and procedures for data transformations will be subsequently studied

Part 9 of 10

Goal 1 Statement: Review the use of piecewise functions for predictive and forecasting purposes

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

NOTE: Specific methods and procedures for the use of piecewise functions for predictive and forecasting purposes will be subsequently studied

Part 10 of 10

Goal 1 Statement: Review procedures for choosing the type of function(s) (linear, polynomial, exponential, logarithmic, logistic, power, and/or sinusoidal) for predictive and forecasting purposes

Goal 1 Plan: Read source materials

Goal 1 Work Product: None

Goal 1 Result: Completed

Goal 2 Statement: Review methods for fitting the curve of a type of function (linear, polynomial, exponential, logarithmic, logistic, power, and/or sinusoidal) for predictive and forecasting purposes

Goal 2 Plan: Read source materials

Goal 2 Work Product: None

Goal 2 Result: Completed