Absolute Value Functions
Absolute value functions are explored, using an applet, by comparing the graphs of f(x) and h(x) = f(x).
Function f(x) used is a quadratic function of the form
f(x) = ax^{2} + bx + c
The exploration is carried out by changing the parameters a, b and c included in f(x) above.Interactive Tutorial
 click on the button above "draw" to start.
 Use the sliders to set parameter a to zero, parameter b to zero and parameter c to a positive value; f(x)is a constant function. Compare the graph of f(x) in blue and that of h(x) = f(x) in red. Change c to a negative value and compare the graphs again. Use the definition of the absolute value functions to explain how can the graph of f(x) be obtained from the graph of f(x).

Keep the value of a equal to zero, select non zero values for b to obtain a linear function . How can the graph of h(x) be obtained from that of f(x)?
Hint: use the definition of the absolute value functions and reflection of a graph on the xaxis.
 Set b and c to zero and select a positive value for a to obtain a quadratic function . Why are the two graphs the same? (Hint: use the definition of the absolute value functions).
 Set b and c to zero and select a negative value for a to obtain a quadratic function . Why are the two graphs reflection of each other? (Hint: use the definition of the absolute value functions and reflection of a graph on the xaxis).
 Keep the values of a and b as in 5 above and change gradually c from zero to some positive values. How can the graph of h(x) be obtained from that of f(x)?
 Select different values for a, b and c and explore.
Exercises
Sketch the following functions
 f(x) = x  1 and h(x) = f(x)

f(x) = x^{2}  4 and h(x) = f(x)
 f(x) = x and h(x) = f(x)
You will find more pages in this web site related to absolute value functions and equations.

