Right answer:
B) 1/4
A function [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs). On the other hand, the absolute value function [tex]f(x)=\left | x \right |[/tex] is a Piecewise Function defined as:
[tex]f(x)=\left|x\right|=\left\{ \begin{array}{c} x\ \ \ \ if\,x\geq0\\ -x\ \ \ if\,x<0 \end{array}\right.[/tex].
For a function [tex]f(x)=a\left | x \right |[/tex]:
- If [tex]\left | a \right |[/tex] is small, the graph of the function opens more widely than if [tex]\left | a \right |[/tex] is large. Finally, the correct option is B) 1/4
[tex]\boxed{f(x)=\frac{1}{4}\left | x \right |}[/tex]
