Function Properties and Elementary Functions
Function properties (increasing and decreasing, bounded, maximum and minimum, even and odd, one-to-one), quadratic functions and quadratic inequalities, absolute value functions, rational and power functions, and inverse functions. Algebra 2 / Year 11 level.
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Available exercises
Function properties from a graph
Use the graph to decide where the function is increasing or decreasing, whether it is bounded, what its maximum is and whether it is one-to-one.
Even and odd functions
Decide from the formula or from the graph whether a function is even, odd or neither.
Vertex and intercepts of a parabola
Complete the square to find the vertex of a parabola, its axis of symmetry and where the graph crosses the axes.
Match the equation to the parabola
Read the vertex, direction and width from the graph of a parabola and choose the correct formula.
Quadratic inequalities
Solve a quadratic inequality using its roots and the parabola, and choose the correct interval.
Absolute value functions and equations
Match a formula to the graph of y = |x − a| + b and solve equations with absolute value.
Rational and power functions
Find the asymptotes of a hyperbola, match a formula to a graph and decide on the properties of power functions.
One-to-one and inverse functions
Decide whether a function is one-to-one, find the formula of the inverse function and points on its graph.