Answer:
Option 2.
Step-by-step explanation:
We need to find a function g(x) which has x-intercepts at (1/2,0) and (6,0).
To find the x-intercepts substitute g(x)=0 in function.
For option 1,
[tex]2(x + 1)(x + 6)=0[/tex]
Using zero product property we get
[tex](x + 1)=0[/tex] and [tex](x + 6)=0[/tex]
[tex]x=-1[/tex] and [tex]x=-6[/tex]
Therefore the x-intercepts of this function at (-1,0) and (-6,0).
For option 2,
[tex](x-6)(2x-1)=0[/tex]
Using zero product property we get
[tex]x-6=0[/tex] and [tex]2x-1=0[/tex]
[tex]x=6[/tex] and [tex]x=\frac{1}{2}[/tex]
Therefore the x-intercepts of this function at (1/2,0) and (6,0).
For option 3,
[tex]2(x-2)(x-6)=0[/tex]
Using zero product property we get
[tex](x -2)=0[/tex] and [tex](x -6)=0[/tex]
[tex]x=2[/tex] and [tex]x=6[/tex]
Therefore the x-intercepts of this function at (2,0) and (6,0).
For option 4,
[tex](x + 6)(x + 2)=0[/tex]
Using zero product property we get
[tex](x +6)=0[/tex] and [tex](x +2)=0[/tex]
[tex]x=-6[/tex] and [tex]x=-2[/tex]
Therefore the x-intercepts of this function at (-2,0) and (-6,0).
Therefore, the correct option is 2.
