Function Fundamentals

Topics Description
Functions: Definitions, Notation & Terminology We learn what a function is, how it works and how to calculate the "output" value it produces when an "input" value is placed inside it. The term "mapping" is introduced as well as the terms "domain" and "range".
Curve of a Function We learn how to use a table of values to calculate the coordinates of points the function's curve passes through in order to draw its curve.
Plotting Curves & finding "key point" with Graphical Display Calculator (GDC) - TI NSpire CX We learn how to use the TI NSpire CX calculator to:
  • plot a function's curve
  • adjust the window settings to view the curve properly
  • find the zeros of a function (the points at which the curve cuts the \(x\)-axis)
  • find the coordinates of a curve's maximum or minimum point
Domain & Range of a Function We learn how to find the domain and the range of a function by looking at its curve
Domain of a Function Given a function's equation, we learn how to find its domain algebraically.
Vertical Line Test How to check whether a curve represents a function \(f(x)\), simply by drawing a vertical line.
Mappings & Horizontal Line Test We define one-to-one and many-to-one mappings and learn a graphical method for checking whether a mapping is one-to-one or many-to-one mapping.
Composite Functions Given two functions \(f(x)\) and \(g(x)\) we learn how to find the expressions for the composite functions \(f\begin{pmatrix}g(x)\end{pmatrix}\) and \(g\begin{pmatrix}f(x)\end{pmatrix}\).
Inverse Functions - Part 2 Given a function \(f(x)\), we learn how to find its inverse function, \(f^{-1}(x)\), algebraically. The method is taught in detail for linear, rational and quadratic functions.

Quadratic Functions - Parabola

Topics Description
Quadratic Functions - The Parabola We learn about the features of a parabola: concavity, \(y\)-intercept, axis of symmetry, vertex, \(x\)-intercepts
Finding a Parabola's Equation using Root Factoring In this section we learn how to find the equation of a parabola, \(y=ax^2+bx+c\), using its \(x\)-intercepts to write it in root-factored form \(y=a(x-p)(x-q)\) or \(y=a(x-p)^2\).
How to Find the Equation of a Parabola using its Vertex - Vertex Form We learn how to use the coordinatesa parabola's vertex, which can be either a minimum or a maximum point, to find its equation.
Form
Sketching a Parabola Without a Calculator

Transforming Functions' Curves

Topics Description
Vertical & Horizontal Translations We learn how to translate, or shift, a function's curve both horizontally and vertically. The rule, or method, is clearly explained and illustrated with tutorials and worked examples.
Vertical & Horizontal Strectches.
Reflections across the \(x\) and \(y\) axes.
Combination of Transformations
Finding Transformations

Circular Functions

Topics Description
Unit Circle: definition of \(cos(x)\) and \(sin(x)\) We define both \(cos(x)\) and \(sin(x)\) using the unit circle and learn how to use the unit circle to find values of \(sin(x)\) and \(cos(x)\), corresponding to angles in each of the four quadrants around the circle.
A tutorial has been made for each quadrant of the unit circle.
Unit Circle: definition of \(tan(x)\)
Cosine and Sine curves: \(y = cos(x)\) and \(y=sin(x)\)
The wave function: \(y=a.cos\begin{pmatrix}b(x-c)\end{pmatrix}+d\) and \(y=a.sin\begin{pmatrix}b(x-c)\end{pmatrix}+d\)