## MAT135 Unit 1: Functions

**1.1 FUNCTIONS AND CHANGE**

Domain and Range

Linear Functions

Increasing / Decreasing Functions (+"Monotonic")

Proportionality (aka "Direct Variation")

**1.2 EXPONENTIAL FUNCTIONS**

Exponential Growth (i.e. of a population)

Concavity

Exponential Decay (i.e. of a drug in the body)

Half-Life and Doubling Time

Base e

**1.3 NEW FUNCTIONS FROM OLD**

Shifts and Stretches

Composite Functions

Odd and Even Functions: Symmetry

Inverse Functions

**1.4 LOGARITHMIC FUNCTIONS**

Logarithms to Base 10 and to Base e

Solving Equations Using Logarithms

**1.5 TRIGONOMETRIC FUNCTIONS**

Radians

The Sine and Cosine Functions

The Tangent Function

The Inverse Trigonometric Functions

**1.6 POWERS, POLYNOMIALS, AND RATIONAL FUNCTIONS**

Power Functions

Exponential vs Power Functions (Exponential Dominates)

Polynomial Functions

Rational Functions (including Horizontal and Vertical Asymptotes)