# Functions

The topic is divided into the following subtopics:
• Properties of functions
• Linear functions
• 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

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