# Graphing |f(x)| and f(|x|)

The absolute value of x written as |x| is the "length" of x which can only be positive. For example, |-7|=7 , |1|=1 ,and |-4|=4 ; the pattern is quite clear: the absolute value of a negative number is positive. In this section we consider the graph of f(x) and discuss how to graph |f(x)| and f(|x|) .

## Calculate |f(x)| and f(|x|): Quadratic Equation

Use the interface as an exercise by hiding the answer, fill in the table and then check your answer by pressing the red "show answer" button. Plot the (x,y) coordinate for each calculate point. Can you discern a pattern.

y=function x value y value
f(x)=x2-x-20
|f(x)|=|x2-x-20|
f(|x|)=|x|2-|x|-20
f(x)=x2-x-20
|f(x)|=|x2-x-20|
f(|x|)=|x|2-|x|-20

## Graph of |f(x)| and f(|x|): Quadratic Equations

The graph shows a quadratic equation f(x). Sketch both |f(x)| and f(|x|) on paper, then press show to check your graphs.

### Discussion

The graph of f(x) below the x-axis is reflected to plot the graph of |f(x)|, the two function are identical when f(x)>0. The graph of f(x) for x>0 is reflected along the y-axis to plot the graph of f(|x|) which is a symmetric function.