State the domain, range and zeros of each of the following.

Question

Answer 1

Observe the graph it is a smooth curve and it has no breaks or corners.

From end behavior of the above graph :

The graph falls to the right and rises to the left and ends that head off in opposite directions.

Therefore, the polynomial function is odd degree polynomial with negative leading coefficient.

The graph crosses the x - axis at (-3, 0)(-1, 0)(2, 0).

So the zeros of the function  at x = -3, -1 ,2

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

The function is y = - x³  - 2x² + 5x + 6

Domain of the odd degree polynomials is all real numbers

Range is also all real numbers.

 

Comments

where did you get 3,1, and -2.

how did ''f(x) = - (x + 3)(x + 1) (x - 2)'' come about?

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Observe that graph, the curve intersect the x axis is at -3,-1, and 2

(x-(-3))(x-(-1))(x-2)