1. Chapter 1 1.1 Lines Increments Δx, Δy Slope m = (y2 - y1)/(x2 - x1)
Point-slope Equation y = m(x – x1) + y1
Slope-intercept equation y = mx + b
General Equation Ax + By = C

2. Chapter 1 1.2 Functions and Graphs Function Vertical Line Test
Even Functions f(-x) = f(x)
Odd Functions f(-x) = -f(x)
Symmetry
Composite Functions f(g(x))
Types of Functions Piece, Absolute Value
Domain and Range

3. Chapter 1 1.3 Exponential Functions f(x) = ax Domain and Range
Rules for exponents
ax ay = ax+y ax/ay = ax-y (ax)y = axy a-x=1/ax a0=1
Exponential Growth/Decay y = yObt/h
The number e

4. Chapter 1 1.4 Parametric Equations x = f(t), y = f(t)
Parametric Curves Circles, Ellipses, Hyperbolas
Eliminating the parameter
Substitution
Trigonometric Identity

5. Chapter 1 1.4 Functions and Logarithms Domain and Range
One-to-one, Horizontal Line Test
Finding Inverses
Logarithms
y = logax if x = ay logaa = 1 loga1 = 0
logars = logar + logas logar/s = logar - logas
logarc = c logar logbx = logax/logab

6. Chapter 1 1.5 Trigonometric Functions
Graphs of Trigonometric Functions
Period
Transformations y = a f(b(x + c)) + d
Identities
Graphs of Inverse Trigonometric Functions

7. Chapter 2 2.1 Rates of Change Average and Instantaneous Speed
Definition of a Limit
Limit Properties
Sandwich/Pinching Theorem

8. Chapter 2 2.2 Limits at Infinity Horizontal Asymptotes
Vertical Asymptotes
End Behavior
3 Rules

9. Chapter 2 2.3 Continuity Removable, Jump, Infinite, Oscillating
Intermediate Value Theorem
Properties of Continuous Functions

10. Chapter 2 2.4 Rates of Change and Tangent Lines
Average Rates of Change
Slope of a Curve
Properties of Continuous Functions
Normal and Tangent Lines

11. Chapter 3 3.1 Derivatives Definition Notation
Graphing Derivatives from data/lines
One Sided Derivatives

12. Chapter 3 3.2 Differentiability Nondifferentiable
Breaks
Corners
Cusps
Vertical Tangents
Intermediate Value Theorem for Derivatives

13. Chapter 3 3.3 Rules for Derivatives Constant Rule Power Rule
Constant Multiple Rule
Sum and Difference Rule
Product Rule
Quotient Rule

14. Chapter 3 3.4 Velocity and Other Rates of Change
Instantaneous Velocity
Speed
Acceleration
Marginal Cost/Marginal Revenue

15. Chapter 3 3.5 Derivatives of Trigonometric Functions
d/dx sin x = cos x
d/dx cos x = -sin x
d/dx tan x = sec2x
d/dx cot x = -csc2x
d/dx sec x = sec x tan x
d/dx csc x = -csc x cot x

16. Chapter 3 3.6 Chain Rule d/dx f(g(x)) = f’(g(x))•g’(x)2.
3. Finding Slope of Parametric Curves

17. Chapter 3 3.7 Implicit Differentiation
Used when y cannot be solved in terms of x.
Used for fractional exponents.

18. Chapter 3
3.8 Derivatives of Inverse Trigonometric Functions

19. Chapter 3 3.9 Derivatives of Exponential and Logarithmic Functions
d/dx ex = ex
d/dx ax = ax ln a
d/dx ln x = 1/x
d/dx logax = 1/a (ln a)
Logarithmic Differentiation

20. Chapter 4 4.1 Extreme Values Absolute Extrema Extreme Value Theorem
Local Extrema
Critical Points

21. Chapter 4 4.2 Mean Value Theorem Mean Value Theorem for Derivatives
f’(c) = (f(b) – f(a)) /(b – a)
Increasing/Decreasing Functions
Antiderivatives

22. Chapter 4 4.3 Connecting f’(x) with f’’(x) First Derivative Test
Second Derivative Test
Concavity
Inflection Points

23. Chapter 4 4.4 Optimization Max-Min Problems Box Can Inscribed Figures
Distance
Fence

24. Chapter 4 4.5 Linearization Linearization L(x) = f(a) + f’(a)(x - a)
Newton’s Method xn = xn-1 – f(xn)/f’(xn)
Differentials dy = f(x) dx
Absolute, Relative, and Percentage Change.

25. Chapter 4 4.6 Related Rates Balloon Ladder Box Conical Tank
Highway Chase
Rope