Functions I
Explore a comprehensive tutorial covering different types of functions, including linear, quadratic, exponential, hyperbolic, sine, cosine, and tangent, and their characteristics such as domain, range, notation, and graphing.
Introduction to Functions
Set Notation
Interval Notation
Function Notation
Representations of Functions
Domain and Range
Functions of the Form <em>y = x</em>
Functions of the Form <em>y = mx + c</em>
Discovering the Characteristics of Linear Functions
Sketching Graphs of the Form <em>y = mx + c</em>
Dual Intercept Method
Gradient and <em>y</em>-intercept Method
Functions of the Form <em>y = x<sup>2</sup></em>
Functions of the Form <em>y = ax<sup>2</sup> + q</em>
Discovering the Characteristics of Quadratic Functions
Sketching Graphs of the Form <em>y = ax<sup>2</sup> + q</em>
Functions of the Form <em>y = <sup>1</sup>/<sub>x</sub></em>
Functions of the Form <em>y = <sup>a</sup>/<sub>x</sub> + q</em>
Discovering the Characteristics of Hyperbolic Functions
Sketching Graphs of the Form <em>y = <sup>a</sup>/<sub>x</sub> + q</em>
Functions of the Form <em>y = b<sup>x</sup></em>
Functions of the Form <em>y = ab<sup>x</sup> + q</em>
Discovering the Characteristics of Exponential Functions
Sketching Graphs of the Form <em>y = ab<sup>x</sup> + q</em>
Functions of the Form <em>y = sin θ</em>
Functions of the Form <em>y = a sin θ + q</em>
Discovering the Characteristics of Sine Functions
Functions of the Form <em>y = cos θ</em>
Functions of the Form <em>y = a cos θ + q</em>
Discovering the Characteristics of Cosine Functions
Comparison of graphs of <em>y = sin θ</em> and <em>y = cos θ</em>
Functions of the Form <em>y = tan θ</em>
Functions of the Form <em>y = a tan θ + q</em>
Discovering the Characteristics of Tangent Functions
Interpretation of Graphs
Summary and Main Ideas