Functions

The topic is divided into the following subtopics:

Properties of functions
Linear functions
Quadratic functions
Linear functions with absolute values
Power and radical functions
Rational functions, inverse proportionality

Properties of functions

Part I:

Properties of functions given by a table or a graph (parity, monotonicity, minima, maxima)

Part II:

Properties of functions given by equations – practicing through various types of functions (linear, quadratic, with absolute values, rational)
Domains of composite functions

Part III:

One-to-one function and inverse function

Linear functions

Part I:

Properties of linear functions and of their restrictions (domain, range, monotonicity, intercepts with axis, … )
Function values
Equation of a linear function
Verifying if the given point lies on a graph of a function

Part II:

Transformations of a graph of a linear function
Solving linear equations with aid of graphs of linear functions

Part III:

Finding equation of a linear function (complex problems)
Linear functions with parameter
Word problems

Quadratic functions

Part I:

Properties of quadratic functions (domain, range, intercepts with axis, monotonicity, …)
Determining of function values
Matching graphs to equations of corresponding functions

Part II:

Transformations of a graph of a quadratic function
Determining of the equation of a function given by three points
Determining of the vertex of a parabola
Solving quadratic equations and inequalities with an aid of graphs of quadratic functions

Part III:

Quadratic functions with parameter
Quadratic functions with absolute values
Solving quadratic equations and inequalities with absolute value with an aid of graphs of quadratic functions
Word problems

Functions with absolute values

Part I:

Properties of absolute value function
Function f(x)=a|x-b|+c, where a, b, c are real numbers

Part II:

Functions with absolute values and their graphs
Properties of functions with absolute value (domain, range, monotonicity, extremes, boundedness, parity)

Part III:

Function with an absolute value inside an absolute value

Power and radical functions

Part I:

Power functions with integer exponent

Determining function value
Graphs of functions and their transformations
Properties of functions (domain, range, monotonicity, extremes, boundedness, parity)
Inequalities assessments with an aid of graphs of functions

Part II:

Nth-root function

Part III:

Functions with absolute values
Word problems

Rational functions

Part I:

Inverse proportionality

Graph of the function
Function value
Word problems

Part II:

Linear rational function

Function’s graph and its transformations
Center of a hyperbola
Properties of functions (domain, range, monotonicity, extremes, boundedness, parity)

Part III:

Rational function
Functions with absolute values
Problems with parameters
Word problems