Answer:
Option: C is the correct answer.
[tex]f(x)=x^3+x^2-9x-9[/tex]
Step-by-step explanation:
Clearly from the graph we could see that:
3 and -3 are zeros of the function f(x).
since the graph crosses these two points on the x-axis.
i.e. when x=3 or -3 ⇒ f(x)=0
Now when we put x=3 in each of the equation we see that:
A)
[tex]f(x)=x^3+2x^2-4x-8[/tex]
when x=3
[tex]f(x)=3^3+2\times 3^2-4\times 3-8\\\\f(x)=27+18-12-8\\\\f(x)=25\neq0[/tex]
Hence, option A is incorrect.
B)
[tex]f(x)=x^3+4x^2-x-4[/tex]
when x=3
[tex]f(x)=27+36-3-4\\\\f(x)=56\neq0[/tex]
Hence, option B is incorrect.
D)
[tex]f(x)=x^3+3x^2-3x-9[/tex]
when x=3
[tex]f(x)=27+27-9-9\\\\f(x)=36\neq0[/tex]
Hence, option D is incorrect.
Hence all the three options are discarded.
Hence, option C is the correct answer.
The function best represents the graph is:
[tex]f(x)=x^3+x^2-9x-9[/tex]
