Absolute Value Functions

Interactive Tutorial

Your browser is completely ignoring the <APPLET> tag!

1. click on the button above "click here to start" and MAXIMIZE the window obtained.
   
   
2. 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).
   
   
3. 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 x-axis.
   
   
4. 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).
   
   
5. 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 x-axis).
   
   
6. 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)?
   
   
7. Select different values for a, b and c and explore.
   
   

1. f(x) = | x - 1 |
   
2. g(x) = | x² - 4 |
   
3. h(x) = | -x |

You will find more pages in this web site related to absolute value functions and equations.

• Simplify Absolute Value Expressions.
  
  
• Definition of the absolute value.
  
  
• Solve Equations with Absolute Value.
  
  
• Equations And Inequalities with Absolute Value - Problems.
  
  
• Solve Inequalities With Absolute Value - Tutorials.