Calculus I > Precalculus Review
Review Objective
Basic Concepts of Functions
Defining a Function
Intervals
Implied Domain
Even and Odd Functions
Composite functions
Inverse Functions
Polynomial Functions
Linear Functions
Quadratic Functions
Polynomial Function
Rational Functions
Rational Functions
Vertical and Horizontal Asymptote
Exponential and Logarithm
Rational and Irrational Exponents
Exponential Functions
Logarithmic Functions
Laws of Logarithms
Trigonometric functions
Radian and right triangles
Trigonometric functions
Trigonometric functions on a coordinate system
Sine and cosine function
Tangent function
Trigonometric additions and subtractions
Trigonometric formulas
Inverse sine function
Inverse cosine function
Inverse tangent function

Intervals

An interval is a set of real numbers “between two endpoints,” say $ a$ and $ b$. Depending on whether it includes endpoints or not, and whether it is finite or infinite, the following types of an interval are considered.

Finite interval Notation
$ a < x < b$ $ (a,\: b)$
$ a \le x \le b$ $ [a,\: b]$
$ a \le x < b$ $ [a,\: b)$
$ a < x \le b$ $ (a,\: b]$

Infinite interval Notation
$ x > a$ $ (a,\: \infty)$
$ x \ge a$ $ [a,\: \infty)$
$ x < b$ $ (-\infty,\: b)$
$ x \le b$ $ (-\infty,\: b]$

The set of all real numbers can be viewed as a special case of interval, denoted by  $ (-\infty, \infty)$.

© TTU Mathematics