Question

Which of the following does not represent an attribute of the function f(x) = |x|?.

Answer 1

There are different kinds of attributes. The option that is not represent an attribute of the function f(x) = |x| is that the graph has a line of symmetry at y = 0.

Note that:

f(x) = IxI

IxI = x if x ≥ 0

IxI = -x if x ≤ 0.

Why is the statement false

The graph has a line of symmetry at y = 0."  is false  because  the real line of symmetry is at x = 0, y = 0 is in line with the x-axis. Therefore as the graph opens up, we would not be able to have symmetry on any line parallel to the x-axis.

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