Question

The function shown in this graph is f(x)=?

Answer 1

I believe the answer is X^4-2x^2+5x+6

Answer 2

Answer:

The correct option is 2.

Step-by-step explanation:

If the graph of a polynomial intersect the x-axis at $a_1,a_2,...,a_n$, then the polynomial is defined as

$P(x)=a_0(x-a_1)(x-a_2)...(x-a_n)$

From the given graph it is clear that the x-intercepts of the function are -2, 1 and 3. So the required function is

$f(x)=a_0(x+2)(x-1)(x-3)$

The y-intercept of the graph is at (0,6).

$6=a_0(0+2)(0-1)(0-3)$

$6=6a_0$

$1=a_0$

The value of $a_0$ is 1. So the required function is

$f(x)=(x+2)(x-1)(x-3)$

$f(x)=x^3 - 2 x^2 - 5 x + 6$

Therefore the correct option is 2.