The correct reprentation of the given function is required.
The correct option is A.
The given function is
[tex]f(x)=3[/tex] if [tex]x<1[/tex]
[tex]f(x)=x[/tex] if [tex]x\geq 1[/tex]
[tex]f(x)=3[/tex] means [tex]y=3[/tex].
This means it will be a horizontal line at [tex]f(x)=y=3[/tex]
This is used when [tex]x<1[/tex]
This means all the values of [tex]x[/tex] not equal to but less than 3.
So, the starting circle at point [tex](1,3)[/tex] will be hollow and the line will go towards infinity towards the negative direction.
When [tex]x\geq 1[/tex] the function [tex]f(x)=x[/tex]
This means that when [tex]x[/tex] has value greater than or equal to 1.
The value of [tex]f(x)=x[/tex]
This means it will be a straight line from [tex](1,1)[/tex] with slope of 1.
As the sign is [tex]\geq[/tex] the circle will be filled at [tex]x=1[/tex].
Hence, the correct option is A.
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