Functions

Properties of functions

A:

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

B:

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

C:

  • One-to-one function and inverse function

Linear functions

A:

  • 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

B:

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

C:

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

Quadratic functions

A:

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

B:

  • 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

C:

  • 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

Linear functions with absolute values

A:

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

B:

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

C:

  • Function with an absolute value inside an absolute value

Power and radical functions

A:

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

B:

  • Nth-root function

C:

  • Functions with absolute values
  • Word problems

Rational functions

A:

Inverse proportionality
  • Graph of the function
  • Function value
  • Word problems

B:

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

C:

  • Rational function
  • Functions with absolute values
  • Problems with parameters
  • Word problems