Answer:
Option: B is the correct answer.
B) [tex]y=(x-1)(x-3)[/tex]
Step-by-step explanation:
From the graph that is provided to us, we see that the graph passes through .
the points (1,0) and (3,0).
This means that the zero of the function are at x=1 and at x=3
Hence, when x=1 then y=f(x)=0
and similarly
at x=3 we have f(x)=0
Now, we will check in each of the given options:
A)
[tex]y=(x+1)(x-3)[/tex]
when x=1 then, we have:
[tex]y=(1+1)(1-3)\\\\\\y=2\times -2\\y=-4\neq 0[/tex]
Hence, option: B is incorrect.
C)
[tex]y=(x-1)(x+3)[/tex]
when x=3 then, we have:
[tex]y=(3-1)(3+3)\\\\\\y=2\times 6\\y=12\neq 0[/tex]
Hence, option: C is incorrect.
D)
[tex]y=(x+1)(x+3)[/tex]
when x=3 then, we have:
[tex]y=(3+1)(3+3)\\\\\\y=4\times 6\\y=24\neq 0[/tex]
Hence, option: D is incorrect.
B)
[tex]y=(x-1)(x-3)[/tex]
at x=1 and at x=3 we get y=0
Also, the graph of this function matches the given graph.
Hence, the correct answer is option: B
