MATH 1120
Calculus of Functions of One Variable I
Complete Study Guide — All 13 Chapters
Independent Study Resource
Not affiliated with or endorsed by Yale University
Aligned with the Yale MATH 1120 syllabus and Stewart's Calculus: Early Transcendentals topic
sequence
Edition 2026
,Table of Contents
1. Functions, Graphs, and Precalculus Review
2. Limits and Continuity
3. The Derivative: Definition and Interpretation
4. Differentiation Rules
5. Derivatives of Trigonometric, Exponential, and Logarithmic Functions
6. The Chain Rule and Implicit Differentiation
7. Applications: Related Rates and Linear Approximation
8. Curve Sketching and the Shape of Graphs
9. Optimization Problems
10. Antiderivatives and Indefinite Integrals
11. The Definite Integral and Area Under a Curve
12. The Fundamental Theorem of Calculus
13. Introduction to Differential Equations
14. Glossary of Key Terms
15. Formula Sheet
16. Final Exam Strategy and Study Checklist
17. References and Attribution
, Chapter 1 — Functions, Graphs, and
Precalculus Review
Learning Objectives
1. Define a function and identify its domain and range.
2. Evaluate and combine functions (sum, difference, product, quotient, composition).
3. Recognize and graph the standard library of functions.
4. Apply transformations: shifts, stretches, and reflections.
5. Solve equations involving exponential and logarithmic functions.
Key Definitions
Term Definition
Function A rule that assigns to each input exactly one output.
Domain The set of all valid inputs.
Range The set of all outputs.
Composite Function (f ∘ g)(x) = f(g(x)).
Even Function f(−x) = f(x); symmetric about the y-axis.
Odd Function f(−x) = −f(x); symmetric about the origin.
One-to-One Each output corresponds to exactly one input; passes the horizontal line
Function test.
Inverse Function f⁻¹ undoes f; f(f⁻¹(x)) = x.
1.1 The Library of Functions
You must know these functions by shape, domain, and range before beginning calculus:
Calculus of Functions of One Variable I
Complete Study Guide — All 13 Chapters
Independent Study Resource
Not affiliated with or endorsed by Yale University
Aligned with the Yale MATH 1120 syllabus and Stewart's Calculus: Early Transcendentals topic
sequence
Edition 2026
,Table of Contents
1. Functions, Graphs, and Precalculus Review
2. Limits and Continuity
3. The Derivative: Definition and Interpretation
4. Differentiation Rules
5. Derivatives of Trigonometric, Exponential, and Logarithmic Functions
6. The Chain Rule and Implicit Differentiation
7. Applications: Related Rates and Linear Approximation
8. Curve Sketching and the Shape of Graphs
9. Optimization Problems
10. Antiderivatives and Indefinite Integrals
11. The Definite Integral and Area Under a Curve
12. The Fundamental Theorem of Calculus
13. Introduction to Differential Equations
14. Glossary of Key Terms
15. Formula Sheet
16. Final Exam Strategy and Study Checklist
17. References and Attribution
, Chapter 1 — Functions, Graphs, and
Precalculus Review
Learning Objectives
1. Define a function and identify its domain and range.
2. Evaluate and combine functions (sum, difference, product, quotient, composition).
3. Recognize and graph the standard library of functions.
4. Apply transformations: shifts, stretches, and reflections.
5. Solve equations involving exponential and logarithmic functions.
Key Definitions
Term Definition
Function A rule that assigns to each input exactly one output.
Domain The set of all valid inputs.
Range The set of all outputs.
Composite Function (f ∘ g)(x) = f(g(x)).
Even Function f(−x) = f(x); symmetric about the y-axis.
Odd Function f(−x) = −f(x); symmetric about the origin.
One-to-One Each output corresponds to exactly one input; passes the horizontal line
Function test.
Inverse Function f⁻¹ undoes f; f(f⁻¹(x)) = x.
1.1 The Library of Functions
You must know these functions by shape, domain, and range before beginning calculus:
