16 Introduction to Functions

The concept of a function is considered one of the most important concepts in mathematics. A function is a unique relation that transforms an input to an output. The input can be a numerical value, an algebraic expression, a quantity, or some other mathematical object. A functional transformation is a unique, one-to-one correspondence, meaning that each function input maps to one, and only one output. In math we visualize functions as graphs, tables, charts, or symbols. In this module you will develop your understanding of functions and how to manipulate their representations.

16.1 Plotting Functions

  • Ordered Pairs

  • Table of Values

  • Introduction to Functions

  • Functional Notation and Evaluation

  • Is it a function of x?

16.2 Common Functions

  • Linear Functions

  • Quadratic Functions: Characteristics

  • Quadratic Functions: Intercepts

  • Identifying Common Functions

16.3 Properties of Functions

  • Domain and Range

  • Intervals

  • Properties of Curves

  • Symmetry

16.4 Algebra of Functions

  • f+g, f-g, f*g

  • f/g

  • Composition of Functions

16.5 Inverse Functions

  • Is it one-to-one?

  • Finding the Inverse Function

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Topics

1 Whole Numbers
2 Fractions
3 Decimals
4 Ratio & Proportion
5 Tables & Graphs
6 The Real Numbers
7 Solving Linear Equations
8 Graphing Linear Equations
9 Systems of Equations
10 Geometry
11 Polynomials
12 Factoring
13 Rational Expressions & Equations
14 Exponents & Radicals
15 Quadratic Equations
16 Introduction to Functions
19 Exponential and Logarithmic Functions