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) = ax2 + bx + c

The exploration is carried out by changing the parameters a, b and c included in f(x) above.

Interactive Tutorial



a =
-10+10

b =
-10+10

c =
-10+10

>

  1. click on the button above "draw" to start.

  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.

Exercises Sketch the following functions
  1. f(x) = x - 1 and h(x) = |f(x)|
  2. f(x) = x2 - 4 and h(x) = |f(x)|
  3. f(x) = -x and h(x) = |f(x)|

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


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