Question

Which of the following functions best represents the graph?

A. f(x) = x3 + 2x2 − 4x − 8

B. f(x) = x3 + 4x2 − x − 4

C. f(x) = x3 + x2 − 9x − 9

D. f(x) = x3 + 3x2 − 3x − 9

Answer 1

Hello there!
the answer would be A

Hope this helps! :)
~Zain

Answer 2

Option: C is the correct answer.

`f(x)=x^3+x^2-9x-9`

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)

`f(x)=x^3+2x^2-4x-8`

when x=3

`f(x)=3^3+2* 3^2-4* 3-8\\\\f(x)=27+18-12-8\\\\f(x)=25\\eq0`

Hence, option A is incorrect.

B)

`f(x)=x^3+4x^2-x-4`

when x=3

`f(x)=27+36-3-4\\\\f(x)=56\\eq0`

Hence, option B is incorrect.

D)

`f(x)=x^3+3x^2-3x-9`

when x=3

`f(x)=27+27-9-9\\\\f(x)=36\\eq0`

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:

`f(x)=x^3+x^2-9x-9`